eonard is going to construct a pyramid with cardboard for math class. Find how many square inches (in.2) of cardboard he will need. Use 4(1/2)bh+b2 , where b , the base of the pyramid, is 3 in. and h , the height of the pyramid, is 8 in.(1 point)

To find the surface area of the pyramid using the formula you provided, we first need to clarify the components:

- \( b \) is the base of the pyramid. Since you're saying \( b \) is 3 in., we assume it's the area of the base.
- \( h \) is the height of the pyramid, which is given as 8 in.

However, in the formula \( 4(1/2)bh + b^2 \), it seems like \( b \) might also be representing the length of one side of the base if the base is a square pyramid.

1. First, we calculate \( b^2 \):
\[
b^2 = (3 \text{ in})^2 = 9 \text{ in}^2
\]

2. Next, we'll compute the lateral surface area of the pyramid using \( 4(1/2)bh \):
- We first calculate \( (1/2)bh \):
\[
(1/2)bh = (1/2)(3 \text{ in})(8 \text{ in}) = (1/2)(24 \text{ in}^2) = 12 \text{ in}^2
\]

- Now, we multiply by 4 to find the total lateral area:
\[
4 \cdot 12 \text{ in}^2 = 48 \text{ in}^2
\]

3. Finally, we add the base area to the lateral surface area:
\[
\text{Total Area} = \text{Lateral Area} + \text{Base Area} = 48 \text{ in}^2 + 9 \text{ in}^2 = 57 \text{ in}^2
\]

So, Leonard will need a total of **57 square inches of cardboard** for the pyramid.