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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Carrie Buscher*

Carrie has a master's degree in learning disabilities and has taught elementary math for over 20 years.

Your friend Jaden is building a birdhouse made of a rectangular prism and a triangular prism. She wants to know if the red paint she has is enough to paint the outside of the birdhouse. To do this, she needs to find the surface area of the birdhouse.

The first step in finding the surface area of **composite figures**, which are basically just two figures put together, is to separate the figures. For our friend Jaden's birdhouse, this means we have to separate the rectangular prism and the triangular prism. Then we have to find the surface area of each figure. Remember not to include the area of the overlapping parts of each figure. These parts will not be seen and do not need paint applied. Finally, we have to add the surface areas of the rectangular and triangular prisms to find the total surface area.

Step 1: Separate the figures.

Step 2: Find the surface area of each figure.

a. Let's say the rectangular prism of the birdhouse has the following dimensions: length = 8 inches, width = 8 inches and height = 4 inches. Remember the formula for surface area of a rectangular prism is SA = 2(*wl* + *hl* + *hw*). Using this formula, we calculate an answer of 256 square inches.

b. Let's say the triangular prism has a length of 8 inches, a width of 8 inches, a height of 3 inches and a side length of 5 inches. Using the formula for surface area of a triangular prism, SA = *wh* + *lw* + *lh* + *ls*, we calculate a surface area of 152 square inches.

Step 3: Subtract the overlapping parts from each figure.

a. For the rectangular prism: SA - area of the top, so 256 - 64 = 192 square inches.

b. For the triangular prism: SA - area of the base, so 152 - 64 = 88 square inches.

Step 4: Add the adjusted surface areas.

192 + 88 = 280 square inches

Jaden's can of red paint will cover 720 square inches of surface area, so she has enough!

To find the surface area of any composite figures, follow the same steps as the ones we just covered in the last section.

1. Again, we need to separate the figures.

2. Again, we need to find the surface area of each figure.

a. Let's say the cube has 5 faces showing. If the length of a side of the cube is 4 centimeters, each face has an area of 16 square centimeters. Multiply 16 by 5. Now we know the surface area of the cube is 80 square centimeters.

b. Next, find the surface area of the cylinder using the formula SA = 2(pi)(r)(h) + 2(pi)*r* 2 . If the radius of the cylinder is 1 centimeter and the height is 3 centimeter, SA = 2(pi) x 1 x 3 + 2(pi) x 1, giving us 25.13 square centimeters.

3. This next part may get tricky! Think about a cylinder sitting on top of a cube. You'll need to not include the bottom of the cylinder and subtract the area of the bottom of the cylinder from the area of the square on top of the cube.

Find the area of the base of the cylinder using A = (pi)*r* 2 . Subtract your answer from the 80 square inches for the cube and the area of the cylinder.

80 - 6.28 = 73.72 square centimeters

25.13 - 6.28 = 18.85 square centimeters

4. Add the surface areas of each figure to get the total area of the composite figures.

73.72 + 18.85 = 92.57 square centimeters.

Let's take a few moments to review what we've learned about finding the surface area of **composite figures**, which are basically just two figures put together. Finding the surface area of composite figures may seem difficult, but breaking the figures apart makes it much easier. The steps are easy to remember, but let's quickly recap them.

- Step 1: Separate the figures
- Step 2: Find the surface area of each figure
- Step 3: Subtract the overlapping parts from each figure
- Step 4: Add the adjusted surface areas

Simple, right?

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8 in chapter 19 of the course:

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