Question

Molly is painting a model house and needs to know how much paint she will need. She knows the surface area of the prism is 216 square inches and the surface area of the pyramid is 84 square inches.

What is the area Molly needs to paint? Follow the steps to solve this problem.
1. Which surface is shared by the two solids? What are the dimensions of this surface?
The surface that is shared by the two solids is the top of the cube that is the same as the square base of the pyramid.
2. There is another surface that Molly does not need to paint, because it won’t show when she displays the model house. Describe that surface, and explain why it doesn't need to be painted.
She doesn't need to paint the bottom because you cant see the bottom.
3. To find the area Molly needs to paint, she should add the surface areas of both solids and subtract:
Circle the correct answer.
twice the area of the triangle
twice the area of the square
three times the area of the square
the area of the square
4. Find the area Molly needs to paint. Show your work, and be sure to include units with your answer.

Answer 1

Molly needs to calculate the total paintable area by adding the surface areas of both the prism (216 sq inches) and the pyramid (84 sq inches), then subtracting the area of the square base that they share, which is not painted. The total area she needs to paint is 264 square inches.

Step-by-step explanation:

To find the area Molly needs to paint, the correct answer to subtract is: the area of the square.

Work for calculating the total paintable area:

• Surface area of the prism = 216 square inches
• Surface area of the pyramid = 84 square inches
• Shared surface area (base of the pyramid/top of the prism) = side × side
  = 6 inches × 6 inches (assuming it's a square based on the context)
• Now calculate that area: 6 inches × 6 inches = 36 square inches (This is the area of the square base which is shared and is thus only subtracted once)
• Total paintable area = (Surface area of the prism + Surface area of the pyramid) - Area of the square
  = (216 + 84) - 36
  = 300 - 36
  = 264 square inches.

Molly will need enough paint to cover an area of 264 square inches.

Answer 2

Step-by-step explanation:

Part 1) The surface that is shared by the two solids is the top of the cube that is the same that the square base of the pyramid

Part 2) The dimensions of this surface are 6 in x 6 in

Part 3) Molly needs to paint 228 square inches

The picture of the question in the attached figure

Part 1) Which surface is shared by the two solids?

we know that

The surface that is shared by the two solids is the top of the cube that is the same that the square base of the pyramid

Part 2) What are the dimensions of this surface?

The surface is a square with side length 6 inches

so

The dimensions of this surface are 6 in x 6 in

Part 3) what is the area molly needs to paint?

we know that

The area that Molly needs to paint is equal to the surface area of the cube plus the surface area of the pyramid minus two times the area of the surface that is shared by the two solids

so

therefore

Molly needs to paint 228 square inches