Question

Carol is going to make a wooden pyramid and then paint it. She drew the net of a square pyramid as shown below to help her plan the project. What should be the total surface area in square feet of Carol's pyramid?
1. 15.0
2. 21.0
3. 24.0

Answer 1

The given pyramid's total surface area is 3. 24.0 square feet.

Step-by-step explanation:

Step 1:

To calculate the surface area of the given figure, we need to find the surface areas of the different shapes in the figure.

There are 3 triangles and 1 square in the figure.

Step 2:

All the triangles are similar.

The surface area of a triangle = $\frac{1}{2} (baselength)(height).$

The similar triangles have a base length of 3 feet and a height of 2.5 feet.

The surface area of 1 similar triangle = $\frac{1}{2} (3)(2.5)= 3.75$ square feet.

The surface area for all the similar triangles = $3.75 (4) = 15$ square feet.

Step 3:

The surface area of a square is the square of its side length. The square has a side length of 3 feet.

The surface area of the square = $a^{2} = 3^{2} =9$ square feet.

Step 4:

To calculate the total surface area we sum up all the individual surface area.

The total surface area = $15 + 9 = 24$ square feet which is the third option.