How To Find The Surface Area Of Composite Figures?

Have you ever wondered how to find the surface area of a composite figure? Composite figures are made up of multiple simpler shapes, and finding their surface area can be a bit tricky. But don’t worry, we’re here to help! In this article, we’ll walk you through the steps of finding the surface area of composite figures, and we’ll provide some examples to help you understand the process. By the end of this article, you’ll be a pro at finding the surface area of composite figures!

Step Formula Example
1. Find the surface area of each individual shape. A = SA1 + SA2 + SA3… A = 100 cm2 + 150 cm2 + 200 cm2 = 450 cm2
2. Add the surface areas of the individual shapes to find the total surface area of the composite figure. A = SAtotal A = 450 cm2

The surface area of a composite figure is the total area of all the faces of the figure. To find the surface area of a composite figure, you need to find the area of each face and then add them together.

In this tutorial, we will learn how to find the surface area of composite figures using two different methods:

  • The addition method
  • The formula method

We will also look at some examples of composite figures and how to find their surface area.

What is a composite figure?

A composite figure is a two-dimensional shape that is made up of two or more simpler shapes. For example, a rectangle with a semicircle on top is a composite figure.

The simplest composite figures are made up of two rectangles. For example, a square with a rectangle on top is a composite figure.

More complex composite figures can be made up of many different shapes. For example, a house is a composite figure that is made up of a rectangle, a triangle, and a semicircle.

How to find the surface area of a composite figure?

There are two main methods for finding the surface area of a composite figure:

  • The addition method
  • The formula method

The addition method is the simplest method and is the one that we will use in this tutorial. The formula method is more complex, but it can be used to find the surface area of more complex composite figures.

The addition method

To find the surface area of a composite figure using the addition method, you simply add the surface areas of the individual shapes that make up the figure.

For example, if you have a composite figure that is made up of a rectangle and a triangle, you would find the surface area of the rectangle and the triangle separately and then add them together.

The surface area of a rectangle is equal to the length times the width. The surface area of a triangle is equal to half the base times the height.

So, if you have a rectangle with a length of 5 units and a width of 3 units, the surface area of the rectangle would be 5 * 3 = 15 square units.

If you have a triangle with a base of 4 units and a height of 2 units, the surface area of the triangle would be 1 / 2 * 4 * 2 = 4 square units.

So, the total surface area of the composite figure would be 15 + 4 = 19 square units.

The formula method

The formula method for finding the surface area of a composite figure is more complex than the addition method. However, it can be used to find the surface area of more complex composite figures.

The formula for finding the surface area of a composite figure is:

“`
Surface Area = (Area of Shape 1) + (Area of Shape 2) + … + (Area of Shape n)
“`

where n is the number of shapes that make up the composite figure.

For example, if you have a composite figure that is made up of a rectangle and a triangle, the formula for finding the surface area would be:

“`
Surface Area = (Area of Rectangle) + (Area of Triangle)
“`

The surface area of a rectangle is equal to the length times the width. The surface area of a triangle is equal to half the base times the height.

So, if you have a rectangle with a length of 5 units and a width of 3 units, the surface area of the rectangle would be 5 * 3 = 15 square units.

If you have a triangle with a base of 4 units and a height of 2 units, the surface area of the triangle would be 1 / 2 * 4 * 2 = 4 square units.

So, the total surface area of the composite figure would be 15 + 4 = 19 square units.

Examples

Here are some examples of composite figures and how to find their surface area using the addition method and the formula method:

Example 1

A composite figure that is made up of a rectangle and a triangle.

Addition method

The surface area of the rectangle is 5 * 3 = 15 square units.

The surface area of the triangle is 1 / 2 * 4 * 2 = 4 square units.

So, the total surface area of the composite figure is 15 + 4 = 19 square units.

Formula method

The surface area of the composite figure is:

“`
Surface Area = (Area of Rectangle

3. Examples of composite figures

A composite figure is a figure that is made up of two or more simple figures. Some examples of composite figures include:

  • A rectangle with a square on top
  • A triangle with a semicircle on the bottom
  • A trapezoid with a circle on each end

**

4. Tips for finding the surface area of composite figures**

Here are a few tips for finding the surface area of composite figures:

  • Be careful to identify all of the individual shapes that make up the composite figure.
  • Make sure to use the correct formula for each shape.
  • Be careful to add or subtract the areas of the individual shapes correctly.

5. Formulas for finding the surface area of composite figures

The following are formulas for finding the surface area of some common composite figures:

  • Rectangle with a square on top:

“`
SA = 2lw + 2lh + l2
“`

where:

  • SA is the surface area of the composite figure
  • l is the length of the rectangle
  • w is the width of the rectangle
  • h is the height of the square
  • Triangle with a semicircle on the bottom:

“`
SA = bh + 1/2r2
“`

where:

  • SA is the surface area of the composite figure
  • b is the base of the triangle
  • h is the height of the triangle
  • r is the radius of the semicircle
  • Trapezoid with a circle on each end:

“`
SA = 2bh + 2r
“`

where:

  • SA is the surface area of the composite figure
  • b is the base of the trapezoid
  • h is the height of the trapezoid
  • r is the radius of the circle

**

6. Examples of how to find the surface area of composite figures**

Now that we have some formulas for finding the surface area of composite figures, let’s look at some examples of how to use them.

Example 1: Find the surface area of a rectangle with a square on top. The rectangle is 10 inches long and 5 inches wide. The square is 3 inches long and 3 inches wide.

“`
SA = 2lw + 2lh + l2

= 2(10)(5) + 2(10)(3) + 102

= 100 + 60 + 100

= 260 in2
“`

Example 2: Find the surface area of a triangle with a semicircle on the bottom. The triangle is 6 inches long and 4 inches high. The semicircle has a radius of 2 inches.

“`
SA = bh + 1/2r2

= 6(4) + 1/2(2)2

= 24 + 6

38.4 in2
“`

Example 3: Find the surface area of a trapezoid with a circle on each end. The trapezoid is 8 inches wide at the top and 6 inches wide at the bottom. It is 10 inches long. The circles have a radius of 2 inches.

“`
SA = 2bh + 2r

= 2(8)(10) + 2(2)

= 160 + 4

176.2 in2
“`

**

7. **

In this article, we learned how to find the surface area of composite figures. We looked at some examples of composite figures and formulas for finding their surface area. We also saw some examples of how to use these formulas to find the surface area of composite figures.

How do I find the surface area of a composite figure?

The surface area of a composite figure is the sum of the surface areas of its individual parts. To find the surface area of a composite figure, you can use the following steps:

1. Identify the individual parts of the figure.
2. Find the surface area of each part.
3. Add the surface areas of the individual parts to find the total surface area of the composite figure.

For example, to find the surface area of a cube with side length s, you would use the following steps:

1. Identify the individual parts of the cube. The cube is made up of 6 square faces.
2. Find the surface area of each part. The surface area of a square with side length s is s^2.
3. Add the surface areas of the individual parts to find the total surface area of the cube. 6 * s^2 = 6s^2

Therefore, the surface area of a cube with side length s is 6s^2.

What are some common composite figures?

Some common composite figures include:

  • Cubes
  • Rectangular prisms
  • Triangular prisms
  • Pyramids
  • Cones
  • Spheres

How do I find the surface area of a composite figure with different shapes?

To find the surface area of a composite figure with different shapes, you can use the following steps:

1. Identify the individual parts of the figure.
2. Find the surface area of each part.
3. Add the surface areas of the individual parts to find the total surface area of the composite figure.

For example, to find the surface area of a composite figure made up of a cube and a triangular prism, you would use the following steps:

1. Identify the individual parts of the figure. The composite figure is made up of a cube with side length s and a triangular prism with base length b, base height h, and slant height l.
2. Find the surface area of each part. The surface area of a cube with side length s is 6s^2. The surface area of a triangular prism with base length b, base height h, and slant height l is b * h + 2 * b * l.
3. Add the surface areas of the individual parts to find the total surface area of the composite figure. 6s^2 + b * h + 2 * b * l

Therefore, the surface area of a composite figure made up of a cube and a triangular prism is 6s^2 + b * h + 2 * b * l.

What are some tips for finding the surface area of composite figures?

Here are some tips for finding the surface area of composite figures:

  • Break the figure down into its individual parts.
  • Find the surface area of each part.
  • Add the surface areas of the individual parts to find the total surface area of the figure.
  • Be careful to account for overlapping surfaces.
  • If you are stuck, try using a diagram or a model to help you visualize the problem.

What are some common mistakes people make when finding the surface area of composite figures?

Some common mistakes people make when finding the surface area of composite figures include:

  • Forgetting to account for overlapping surfaces.
  • Not including all of the surfaces in the figure.
  • Using the wrong formula for the surface area of a particular shape.
  • Making careless mistakes in calculations.

To avoid these mistakes, it is important to be careful and to double-check your work. If you are stuck, try using a diagram or a model to help you visualize the problem.

finding the surface area of composite figures can be a daunting task, but it is made easier by breaking the figure down into simpler shapes. By using the methods outlined in this article, you can easily find the surface area of any composite figure.

Here are some key takeaways to remember:

  • The surface area of a composite figure is the sum of the surface areas of its individual parts.
  • To find the surface area of a prism, you must find the area of each of its faces and add them together.
  • To find the surface area of a pyramid, you must find the area of its base and multiply it by the slant height.
  • To find the surface area of a cylinder, you must find the area of its base and multiply it by its height.
  • To find the surface area of a cone, you must find the area of its base and multiply it by the slant height and pi.

By following these steps, you can easily find the surface area of any composite figure.

Author Profile

Miranda Crace
Miranda Crace
Miranda is the owner and chief event officer of Spoke Events. She started the company after years of planning and styling event for friends and family. When she’s not planning weddings and events, Miranda is likely to be spotted at her favorite coffee shop, laptop in-hand or planning her next vacation. Miranda is also the owner and co-founder of Spoke Events sister company, Flourish.

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