Question

An illustration shows a net diagram. The center of the diagram is a square with dashed lines marking its sides. Each side forms the base of one of four triangles extending outward from the square. The sides of the square measure 3 inches, and the perpendicular height of the triangular faces measures 5 inches.
A chocolate dessert is in the shape of a square pyramid. The pyramid is represented with a net. How many square inches of icing are needed for the faces of the dessert?

(1 point)
Responses

69 in.2
69 in. squared

39 in.2
39 in. squared

30 in.2
30 in. squared

60 in.2

Answer 1

To find the surface area of the square pyramid, we need to calculate the area of the base and the area of the four triangular faces.

1. **Calculate the area of the base:**
The base is a square with sides measuring 3 inches.

\[
\text{Area of the base} = \text{side}^2 = 3 \text{ in} \times 3 \text{ in} = 9 \text{ in}^2
\]

2. **Calculate the area of the triangular faces:**
Each triangular face has a base equal to the side length of the square (3 inches) and a height of 5 inches.

\[
\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 3 \text{ in} \times 5 \text{ in} = \frac{15}{2} \text{ in}^2 = 7.5 \text{ in}^2
\]

Since there are 4 triangular faces, the total area of the triangular faces is:

\[
\text{Total area of triangular faces} = 4 \times 7.5 \text{ in}^2 = 30 \text{ in}^2
\]

3. **Calculate the total surface area of the square pyramid:**
Add the area of the base and the total area of the triangular faces.

\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of triangular faces} = 9 \text{ in}^2 + 30 \text{ in}^2 = 39 \text{ in}^2
\]

So, the amount of icing needed for the faces of the dessert is:

\[
\boxed{39} \text{ in}^2
\]