Question

Leonard is going to construct a pyramid with cardboard for math class. Find how many square inches (in.2)
(
in.
2
)
of cardboard he will need. Use 4(12)bh+b2
4
(
1
2
)
𝑏
ℎ
+
𝑏
2
, where b
𝑏
, the base of the pyramid, is 3 in. and h
ℎ
, the height of the pyramid, is 8 in.(1

Answer 1

To find the amount of cardboard Leonard will need to construct the pyramid, we can use the formula given for the surface area of the pyramid:

\[
4(12)bh + b^2
\]

where:
- \( b \) is the length of the base of the pyramid,
- \( h \) is the height of the pyramid.

Given that \( b = 3 \, \text{in} \) and \( h = 8 \, \text{in} \), we can substitute these values into the formula.

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

2. Calculate \( 4(12)bh \):
\[
4(12)bh = 4(12)(3)(8)
\]
Simplifying inside the parentheses first:
\[
= 4(12)(24) \quad \text{(since } 3 \times 8 = 24\text{)}
\]
Now calculate \( 12 \times 24 \):
\[
= 12 \times 24 = 288
\]
Now multiply by 4:
\[
4 \times 288 = 1152 \, \text{in}^2
\]

3. Now add \( 4(12)bh \) and \( b^2 \):
\[
\text{Total Surface Area} = 1152 + 9 = 1161 \, \text{in}^2
\]

Thus, Leonard will need **1161 square inches** of cardboard to construct the pyramid.