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Area of composite shapes

Here you will learn about the area of composite shapes, including questions involving rectilinear shapes, composite shapes, missing side lengths and unit conversion.

Students will first learn about composite shapes as part of geometry in 3rd grade when they learn how to decompose and find the area of rectilinear shapes.

Students deepen their understanding of area in 4th grade, and extend their learning by finding the area of more complex shapes in 6th grade.

What is the area of composite shapes?

The area of composite shapes is the amount of space inside a shape composed of basic shapes put together. It is measured in square units ( cm^2, m^2, mm^2 etc.).

Composite shapes can also be called compound shapes or composite figures.

To find the area of composite shapes, you must decompose the composite shape into basic shapes, then find the area of each of the basic shapes and add them together.

For example,

Your final answer must be in square units. For example, square centimeters (cm^2), square meters (m^2), square feet (ft^2), etc.

[FREE] Area of Composite Shapes Worksheet (Grade 3 to 8)

Use this worksheet to check your grade 3 to 8 students’ understanding of calculating the area of composite shapes. 15 questions with answers to identify areas of strength and support!

Common Core State Standards

How does this relate to 3rd grade math and 4th grade math?

• Grade 3 – Measurement and Data (3.MD.7, 3.MD.7.d) Relate area to the operations of multiplication and addition; Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.
• Grade 4 – Measurement and Data (4.MD.3) Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
• Grade 6 – Geometry (6.G.1) Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

How to find the area of composite shapes

Here’s how to find the area of composite shapes:

• Break down the composite shape into simpler shapes, such as rectangles, triangles, etc.

Find the measurements and areas of the simpler shapes.

Add the areas of the simpler shapes together.

Write down your final answer with square units.

Area of composite shapes examples

Example 1: all side lengths given (area of a rectilinear figure).

Find the area of the composite shape below:

• Break down the composite shape into basic shapes.

Split the composite shape into two rectangles. You can do this in two ways:

For the purposes of this question you will use the first way.

2 Find the measurements and area of the simpler shapes.

Label the two rectangles A and B.

Area of Rectangle A :

\begin{aligned} \text { Area }_{A} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{A} &=6 \times 5 \\\\ &=30 \end{aligned}

Area of Rectangle B :

\begin{aligned} \text { Area }_{B} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{B} &=9 \times 4 \\\\ &=36 \end{aligned}

3 Add the areas of the simpler shapes together.

\begin{aligned} \text { Composite Area } &=\text{ Area of } A+ \text{ Area of } B \\\\ &= 30+36 \\\\ &=66 \end{aligned}

4 Write down your final answer with square units.

\text{ Area }=66 \mathrm{~m}^{2}

Example 2: missing lengths

Break down the composite shape into simpler shapes.

Split the composite shape into two rectangles and find the area of each rectangle.

You need to calculate the unknown length. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:

If you add together the 3 sides, you will get the length of rectangle A.

4+5+5= 14 \, m

\begin{aligned} \text { Area }_{A} &=\text{ length } \times \text {width } \\\\ \text { Area }_{A} &=14 \times 2 \\\\ &=28 \end{aligned}

The length of the entire composite shape is 10 \, m. You need to subtract the 2 \, m of shape A to get just the length of shape B.

\begin{aligned} \text { Area }_{B} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{B} &=8 \times 5 \\\\ &=40 \end{aligned}

\begin{aligned} \text { Composite Area } &=\text{ Area of } A+\text{ Area of } B \\\\ &=28+40 \\\\ &=68 \end{aligned}

\text{ Area }=68 \mathrm{~m}^{2}

Example 3: word problem

The wall shown below needs to be painted. Each tin of paint covers a distance of 4 square meters. How many tins of paint will be needed to cover the entire wall?

Split the composite shape into three rectangles and find the area of each rectangle.

Label the three rectangles A, B and C.

Notice that rectangle A and C each have a tick mark at the bottom. This means that these sides are congruent, or equal. Therefore, we know the width of rectangle A is 5 \, m.

\begin{aligned} \text { Area }_{A} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{A} &=12 \times 5 \\\\ &=60 \end{aligned}

Rectangle C is congruent to Rectangle A, so you can just double the area of rectangle A.

60 \times 2=120

You need to calculate the unknown width. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:

The entire width of the shape is 13 \, m. If you subtract 5 \, m and 5 \, m \; ( the width of rectangles A and C).

13 - 5 - 5 = 3 \, m

\begin{aligned} \text{ Area }_{B} &=\text { length } \times \text{ width } \\\\ \text{ Area }_{B} &=7 \times 3 \\\\ &=21 \end{aligned}

\begin{aligned} \text { Composite Area } &=\text{ Area of } A+\text{ Area of } B+\text{ Area of } C \\\\ &=60+21+60 \\\\ &=141 \end{aligned}

\text { Area }=141 \mathrm{~m}^{2}

While this is the total area, you need to calculate how many tins of paint will be needed to cover the wall.

If each tin of paint covers a distance of 4 square meters, you need to divide 4 into 141.

141 \div 4=35.25

Since you cannot buy 0.25 of a can of paint, you need to round your answer to 36 tins of paint.

Answer \textbf{= } \bf{36} tins of paint will be needed .

Example 4: composite shapes involving non-rectangular shapes

Split the composite shape into a triangle and rectangle.

Note: This shape is a trapezoid. Another way to find the area of this shape would be to simply use the formula for the area of a trapezoid. For this question, because you are focusing on composite shapes, you will separate the shape into a triangle and a rectangle.

See also: Area of a trapezoid

Label the two shapes A and B.

Area of Triangle A :

\begin{aligned} \text { Area }_{A} &=\cfrac{b \, \times h}{2} \\\\ \text { Area }_{A} &=\cfrac{2 \, \times 8}{2} \\\\ &=8 \end{aligned}

The height of the entire composite shape is 6 \, m. You need to subtract the 2 \, m of shape A to get just the length of shape B.

\begin{aligned} \text { Area }_{B} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{B} &=8 \times 4 \\\\ &=32 \end{aligned}

\begin{aligned} \text{ Composite Area } &=\text{ Area of } A+\text{ Area of } B \\\\ &=8+32 \\\\ &=40 \end{aligned}

\text{ Area }=40 \mathrm{~m}^{2}

Example 5: missing side lengths

Calculate the value of x in the composite shape below:

Split the composite shape into two rectangles.

Find the measurements and area of the simpler shapes.

\begin{aligned} \text { Area }_{A} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{A} &=8 \times 2 \\\\ &=16 \end{aligned}

In this case, you are not given enough information to find the area of Rectangle B.

Add the areas of the simpler shapes.

For this problem, you will need to use subtraction in order to find the area of rectangle B.

\begin{aligned} \text{ Composite Area } &=\text{ Area of } A+\text{ Area of } B \\\\ 48 &=16+\text{ Area of } B \\\\ \text{ Area of } B &=48-16 \\\\ \text{ Area of } B &=32 \end{aligned}

Now that you know the area of rectangle B, you can calculate the value of x.

\begin{aligned} \text{ Area of } B &=l \times w \\\\ 32 &=l \times 4 \\\\ l &=\cfrac{32}{4} \\\\ l &=8 \, m \end{aligned}

Example 6: multi-step word problem

Below is a blueprint for a garden to be created in the middle of town. It will feature a triangular flowerbed and the remainder of the garden will be covered in grass.

Each roll of grass costs \$24 and covers a distance of 3 square meters. How much will it cost to cover the garden with grass?

Split the composite shape into two rectangles. Once you find the area of the two rectangles, you can subtract the area of the triangle.

Label the three shapes A, B and C.

Area of rectangle A :

\begin{aligned} \text { Area }_A & =\text{ length } \times \text{ width } \\\\ \text { Area }_A & =7 \times 2 \\\\ & =14 \mathrm{~m}^2 \end{aligned}

Area of rectangle B :

\begin{aligned} \text{ Area }_{B} &=\text{ length } \times \text{ width } \\\\ \text { Area }_{B} &=11 \times 7 \\\\ &=77 \mathrm{~m}^{2} \end{aligned}

Area of Triangle C :

The height of the triangle is 6 \, m.

You need to calculate the unknown width of the triangle. To do this, you need to use the measurements you are given in the question that are parallel to the unknown side:

The width of the entire composite shape is 11 \, m. You need to subtract the 5 \, m and 4 \, m from 11 \, m to get the width of shape C.

\begin{aligned} \text{ Area }_{C} &=\cfrac{1}{2} \, (\text{ base } \times \text{ height }) \\\\ \text{ Area }_{C} &=\cfrac{2 \, \times \, 6}{2} \\\\ &=6 \, m^{2} \end{aligned}

\begin{aligned} \text{ Composite Area } &=\text{ Area of } A+\text{ Area of } B-\text{ Area of } C \\\\ &=14+77-6 \\\\ &=85 \end{aligned}

\text { Area }=85 \mathrm{~m}^{2}

Teaching tips for area of composite shapes

• Start with simple shapes like two rectangles before moving onto more complex shapes like triangles and trapezoids.
• Instead of worksheets, offer students a variety of ways to practice finding the area of composite shapes. One idea is for students to create composite shapes (either on paper, using manipulatives, or using an interactive website) and have a partner find the area.

Easy mistakes to make

• Using incorrect units for the answer A common mistake is to forget to include square units when asked to find area.
• Forgetting to convert measures to a common unit Before using the formula for calculating the area of a rectangle, you must look at the units given in the question. If different units are given, for example, length = 4 \, m and width = 3 \, cm, you must convert them either both to cm or both to m.

Related area lessons

• Area of isosceles triangle
• Area of a right triangle
• Area of equilateral triangle
• Area of obtuse triangle
• Area of a hexagon
• Area of a pentagon
• Area of irregular shapes

Practice area of composite shapes questions

1. Find the area of the composite shape below:

Split into two rectangles. Find the area of the rectangle and the area of the square and add them together.

Area of A\text{: } 10 \times 5=50

Area of B\text{: } 5 \times 3=15

Composite Area: 50+15=65 \, m^2

2. Find the area of the composite shape below:

Split into two rectangles. Find the area of the smaller rectangle and the larger rectangle and add them together.

Area of B\text{: } 9 \times 6=54

Composite Area: 50+54=104 \, m^2

3. The wall shown below needs to be painted. Each tin of paint covers a distance of 4 square meters. How many tins of paint will be needed to cover the entire wall?

Split into three rectangles:

Area of A\text{: } 15 \times 5=75

Area of B\text{: } 8 \times 2=16

Area of C\text{: } 15 \times 5=75

Composite Area: 75+16+75=166 \, m^2

Then divide by 4 to get the number of tins.

166 \, m^2 \div 4=41.5

Since you can’t buy 0.5 of a tin, the answer will be rounded up to 42 tins.

4. Find the area of the composite shape below:

Split into one rectangle and two triangles:

Since you know the triangles are congruent, you can use the base of the rectangle to find the base of the triangles.

380 \mathrm{~cm} \div 2=190 \mathrm{~cm}

Area of A\text{: } \cfrac{1}{2} \, (190 \times 80)=7,600

Area of B\text{: } \cfrac{1}{2} \, (190 \times 80)=7,600

Area of C\text{: } 170 \times 380=64,600

Composite Area: 7,600+7,600+64,6000=79,800 \mathrm{~m}^2

5. Find the value of x in the composite shape below:

Split into two rectangles:

Area of B\text{: } 4 \mathrm{~mm} \times 11 \mathrm{~mm}=44 \mathrm{~mm}^2

The difference between the total area and the area of rectangle B will give you the area of rectangle A\text{:}

56 \mathrm{~mm}^2-44 \mathrm{~mm}^2=12 \mathrm{~mm}^2

The area of rectangle A divide by its width will give you the missing side length:

12 \mathrm{~mm}^2 \div 3 \mathrm{~mm}=4 \mathrm{~mm}

The difference between the length of rectangle B and the length of rectangle A gives you the value of missing side length x.

11 \mathrm{~mm}-4 \mathrm{~mm}=7 \mathrm{~mm}

6. An architect is developing a blueprint for one floor of a house which is shown below. The shaded region represents the floor and will need to be fully tiled. Each square tile has a width of 12 \, cm. How many tiles will be needed to cover the entire floor?

To find the area of the shaded region, you need to first find the total area of the rectangle. Then find the area of the triangle.

Instead of adding the areas together, here you will be subtracting the areas.

Area of A\text{: } 7 \times 11=77

Area of B\text{: } \cfrac{1}{2} \, (4 \times 3)=6

\begin{aligned} & 77-6=71 \mathrm{~m}^2 \\\\ & 12 \mathrm{~cm}=0.12 \mathrm{~m} \end{aligned}

Area of 1 tile =0.12 \times 0.12=0.0144 \mathrm{~m}^2

71 \div 0.0144=4,930.56 tiles

4,931 tiles

Area of composite shapes FAQs

A composite is a shape composed of basic shapes put together. A composite shape can also be called a compound shape or a composite figure.

The next lessons are

• Area of a quadrilateral

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5.18: Area and Perimeter of Composite Shapes

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Find area and perimeter of figures made up of two or more common shapes.

Area of Composite Shapes

Perimeter is the distance around a shape. The perimeter of any figure must have a unit of measurement attached to it. If no specific units are given (feet, inches, centimeters, etc.), write “units.”

Area is the amount of space inside a figure. If two figures are congruent, they have the same area ( Congruent Areas Postulate ).

A composite shape is a shape made up of other shapes. To find the area of such a shape, simply find the area of each part and add them up.

Area Addition Postulate: If a figure is composed of two or more parts that do not overlap each other, then the area of the figure is the sum of the areas of the parts.

Consider a basic house drawn as a triangle on top of a square. How could you find the area of this composite shape?

Example \(\PageIndex{1}\)

Find the area of the figure below. All angles that look like right angles are right angles.

Divide the figure into a triangle and a rectangle with a small rectangle cut out of the lower right-hand corner.

\(A=A_{\text{top triangle}}+A_{\text{rectangle}}−A_{\text{small triangle}} \\ A=(\dfrac{1}{2} \cdot 6\cdot 9)+(9\cdot 15))−(\dfrac{1}{2}\cdot 3\cdot 6) \\ A&=27+135−9 \\ A&=153\text{ units}^2\)

Example \(\PageIndex{2}\)

Divide the shape into two rectangles and one triangle. Find the area of the two rectangles and triangle. All angles that look like right angles are right angles.

Rectangle #1: \(\text{Area} =24(9+12)=504\text{ units}^2\)

Rectangle #2: \(\text{Area}=15(9+12)=315\text{ units}^2\)

Triangle: \(\text{Area} =15(9)2=67.5\text{ units}^2\)

Example \(\PageIndex{3}\)

Find the area of the entire shape from Example 2 (you will need to subtract the area of the small triangle in the lower right-hand corner).

\(\text{Total Area} =504+315+67.5−\dfrac{15(12)}{2}=796.5 \text{ units}^2\)

Example \(\PageIndex{4}\)

All angles that look like right angles are right angles.

• Divide the shape into two triangles and one rectangle.
• Find the area of the two triangles and rectangle.
• Find the area of the entire shape.
• One triangle on the top and one on the right, the rest of the shape is a rectangle.
• The area of the triangle on top is \(\dfrac{8(5)}{2}=20\text{ units}^2\). The area of the triangle on the right is \(\dfrac{5(5)}{2}=12.5\text{ units}^2\). The area of the rectangle is \(375\text{ units}^2\).
• The total area is \(407.5\text{ units}^2\).

Use the picture below for questions 1-4. The composite shape is formed of a square within a square.

• Find the area of the outer square.
• Find the area of one grey triangle.
• Find the area of all four grey triangles.
• Find the area of the inner square.

Find the areas of the figures below. You may assume all sides are perpendicular.

Find the areas of the composite figures.

Use the figure to answer the questions.

• What is the area of the square?
• What is the area of the triangle on the left?
• What is the area of the composite figure?

Review (Answers)

To see the Review answers, open this PDF file and look for section 10.6.

Additional Resources

Interactive Element

Video: Area of a Triangle (Whole Numbers)

Activites: Area of Composite Shapes Discussion Questions

Study Aids: Perimeter and Area Study Guide

Practice: Area and Perimeter of Composite Shapes

Find Areas - Composite figures

Related Topics: Lesson Plans and Worksheets for Grade 3 Lesson Plans and Worksheets for all Grades More Lessons for Grade 3 Common Core For Grade 3

Videos, examples, solutions, and lessons to help Grade 3 students learn how to find areas by decomposing into rectangles or completing composite figures to form rectangles.

Common Core Standards: 3.MD.6, 3.MD.7a, 3.MD.7b, 3.MD.7c, 3.MD.7d, 3.MD.5

New York State Common Core Math Module 4, Grade 3, Lesson 13 and Lesson 14 Worksheets for Grade 3

Lesson 13 Application Problem Anil finds the area of a 5 inch by 17 inch rectangle by breaking it into 2 smaller rectangles. Show one way that he could have solved the problem. What is the area of the rectangle?

Note: This problem reinforces the strategy of breaking a larger shape apart into 2 smaller shapes to find the total area.

Lesson 13 Concept Development Problem 1: Add using the break apart strategy to find area of a composite shape. Problem 2: Subtract to find area of a composite shape. Problem 3: Subtract to find area of a composite shape with missing side lengths.

Lesson 13 Problem Set

• Each of the following figures is made up of 2 rectangles. Find the total area of each figure. Figure 1: Area of A + Area of B: 18 + _________ = _________ sq units Figure 2: Area of C + Area of D: ________ + _________ = __________ sq units Figure 3: Area of E + Area of F: ________ + _________ = __________ sq units Figure 4: Area of G + Area of H: ________ + _________ = __________ sq units
• The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region. Area of the shaded region: ______ ֠______ = ______ sq cm
• The figure shows a small rectangle cut out of a big rectangle. a. Label the missing measurements. b. Area of the big rectangle: ______ נ______ = ______ sq cm c. Area of the small rectangle: ______ נ______ = ______ sq cm d. Find the area of the shaded region.

Lesson 13 Homework

• Each of the following figures is made up of 2 rectangles. Find the total area of each figure. Figure 1: Area of A + Area of B: _____ + ______ = ______ sq units Figure 2: Area of C + Area of D: _____ + ______ = _______ sq units Figure 3: Area of E + Area of F: _____ + ______ = _______ sq units Figure 4: Area of G + Area of H: _____ + ______ = _______ sq units
• The figure shows a small rectangle cut out of a big rectangle. Find the area of the shaded region.
• The figure shows a small rectangle cut out of a big rectangle.

Lesson 14 Application Problem a. Break apart the shaded figure into 2 rectangles. Then add to find the area of the shaded figure below. b. Subtract the area of the unshaded rectangle from the area of the large rectangle to check your answer in Part (a).

Note: This problem reviews G3–M4–Lesson 13’s concept of finding area of composite shapes. Students may choose to break apart their rectangles in different ways for Part (a).

Lesson 14 Concept Development Problem 1: Choose an appropriate method for finding the area of a composite shape. Problem 2: Solve a word problem involving area of non- rectangular shapes.

Lesson 14 Homework

• Find the area of each of the following figures. All figures are made up of rectangles.
• The figure below shows a small rectangle cut out of a big rectangle. a. Label the side lengths of the unshaded region. b. Find the area of the shaded region.

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Video transcript

How Do You Find the Volume of a Composite Figure?

Composite figures are just a combination of simpler figures in disguise! In this tutorial, you'll see how to break down a composite figure into simpler figures. Then, see how to find the volume of each of those individual figures to find the volume of the entire composite figure. Watch the whole process in this tutorial!

• composite figure
• find shapes
• many shapes

Background Tutorials

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories..

What is a Rectangle?

A rectangle is one of the many fundamental shapes you'll see in math. Rectangles have special properties that can be very useful in helping you solve a problem. This tutorial introduces you to rectangles and explains their interesting qualities!

Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.

What is a Prism?

The term prism is a cool name for a special kind of three-dimensional solid. This tutorial defines the term prism and shows you how to name a prism using the shape of its bases. Check it out!

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

What is a Composite Figure?

Ever notice that some figures look like a combination of multiple other figures? These types of figures are called composite figures. This tutorial introduces you to composite figures and shows you how to break up a composite figure into multiple shapes. Take a look!

What is the Formula for the Volume of a Prism?

Trying to find the volume of a prism? Did you know that there's a formula to find that volume? In this tutorial, you'll learn about the formula for the volume of a prism. Check it out!

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

What is the Formula for the Volume of a Pyramid?

Looking for the formula for the volume of a pyramid? Then check out this tutorial! You'll learn about the formula for the volume of a pyramid and see how to use the formula in an example. Take a look!

Further Exploration

Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems..

How Do You Find the Volume of a Cylinder?

The volume of a cylinder is the amount of space that will fit inside it. You can use the formula for the volume of a cylinder to find that amount! In this tutorial, see how to use that formula and the radius and height of the cylinder to find the volume. Check it out!

• Terms of Use

Calcworkshop

Area of Composite Figures How-To w/ 19 Step-by-Step Examples!

// Last Updated: January 21, 2020 - Watch Video //

In today’s geometry lesson, you’re going to learn all about the area of composite figures.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

You’ll learn how basic polygons (squares, rectangles, etc.) are used to determine the area of many complex figures.

So let’s jump on in!

Did you know that any polygonal region can be divided into nonoverlapping regions?

This means that we can take any complex shape and divide it into known polygons!

Why is this important?

Because the area of the complex shape is equal to the sum of the areas of the divided nonoverlapping regions!

Area Formulas

Together we will learn how to use formulas to find the area of the following basic polygons:

Area of a Rectangle

Area of a Square

Area of a Triangle

Equilateral Triangle

Area of Equilateral Triangle

Parallelogram

Area of a Parallelogram Formula

Rhombus Area Formula

Trapezoid Area Formula

And then, we will use these formulas for finding the area of basic polygons, to find the area of composite figures.

A composite figure, sometimes referred to as complex figures or shapes, as Khan Academy nicely states, is a figure comprised of two or more basic polygons.

Let’s take a look at a basic example to clarify the process. Notice that the given polygon is comprised of both a square and a triangle. Therefore, if we find the area of the square and the area of the triangle separately, then the total area of the polygon is the sum of these two areas.

How To Find The Area Of A Composite Figure

In the video below, you’ll learn how to set up and solve many different types of problems. Including the tricky ones…

…and lastly, you find out how to use ratios and proportions to find area or lengths of geometric figures too.

Video – Lesson & Examples

• Introduction to Video: Area of Polygons and Complex Figures
• 00:00:27 – Formulas for Finding Area of a Rectangle, Square, Triangle, Parallelogram, Rhombus, and Trapezoid
• Exclusive Content for Member’s Only
• 00:12:12 – Find the area of the polygon or the side length given the area (Examples #1-6)
• 00:20:56 – Find the indicated area or length of a polygon (Examples #7-12)
• 00:30:09 – Finding area of composite figures (Examples #13-15)
• 00:40:27 – Using ratios and proportions find the area or side length of a polygon (Examples #16-17)
• 00:49:51 – Using ratios and proportions find the area or length of a diagonal of a rhombus (Examples #18-19)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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Surface Area of Composite Figures

A composite solid is a solid that is composed, or made up of, two or more solids. The solids that it is made up of are generally prisms, pyramids, cones, and cylinders. In order to find the surface area of a composite solid, you need to know how to find the surface area of prisms, pyramids, cones, and cylinders.

To find the surface area of a composite 3D figure, add the areas of each geometric figure making up the composite 3D figure.

1. Separate the composite figure into all of its faces. Remember that there is no face where two figures join. 2. Find the area of each individual face. 3. Add all of the areas together. 4. Write the total surface area with the appropriate square units.

The top pyramid has two surfaces that are triangles with a height of 7 m and a base of 4 m. Its other two triangular surfaces have a height of 7 m and a base of 5 m.

= 63 m 2 for the top.

The bottom pyramid has two surfaces that are triangles with a height of 9 m and a base of 4 m. Its other two triangular surfaces have a height of 9 m and a base of 5 m.

= 81 m 2 for the top.

The total surface area is 63 m 2 + 81 m 2 = 144 m 2 . 

Practice Surface Area of Composite Figures

Practice Problem 1

Practice Problem 2

Practice Problem 3

Surface area: It is the sum of the areas of all the surfaces of a three-dimensional figure.

Lateral area: It is the surface area of the figure, excluding the area of the base(s) of a three-dimensional figure.

Composite solid – a shape composed of a combination of other 3d solids.

Pre-requisite Skills Nets of 3 Dimensional Figures Surface Area of Prisms Surface Area of Pyramids Surface Area of Cylinders Surface Area of Cones Measurement – Perimeter Measurement – Area Circumference and Area of Circles Surface Area of Rectangular Prisms

Related Skills Volume of Pyramids Volume of Prisms Volume of Spheres Volume of Cylinders Volume of Cones Volume of Rectangular Prisms Volume of Composite Figures