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.

1. Which surface is shared by the two solids? What are the dimensions of this surface?

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.

3. To find the area Molly needs to paint, she should add the surface areas of both solids and subtract:

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.

Oh and here's an image to help you out

For question 4, the area Molly needs to paint is found by adding all the surface areas and subtracting the 2 surfaces that will not be painted: base of pyramid and base of prism (outlined in red). According to the picture, these are both squares with 6 by 6 dimensions.

Step 1. Add all surface areas together

Prism: 6 surfaces

Surface area = 216 inches sq

Front = 6 x 6 = 36
Back = 6 x 6 = 36
Top = 6 x 6 = 36
Bottom (base) = 6 x 6 = 36
Side = 6 x 6 = 36
Other side = 6 x 6 = 36

Pyramid: 5 surfaces

Surface area = 84 inches sq

Bottom (base) = 6 x 6 = 36
Front triangle = (6 x 4)/2 = 12
Back = (6 x 4)/2 = 12
Side = (6 x 4)/2 = 12
Other side = (6 x 4)/2 = 12

TOTAL surface area: 216 inches + 84 inches = 300 inches sq

Step 2. Subtract surfaces that are NOT being painted

300 - base of pyramid - base of prism

300 - 2(36)

300 - 72

228 inches sq

Hope this helps!