Question

Surface Area of Pyramids Practice
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Question
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in. and SA
equals 2,800 in2
.(1 point)
in.
Remaining Attempts : 2
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Answer 1

To find the slant height of a square pyramid given the surface area and the length of the base, we can use the formula for the surface area of a square pyramid:

\[
SA = B + \frac{1}{2} \cdot P \cdot l
\]

Where:
- \( SA \) is the surface area,
- \( B \) is the area of the base,
- \( P \) is the perimeter of the base,
- \( l \) is the slant height.

For a square base:

1. The area of the base, \( B \), is \( s^2 \) where \( s \) is the length of the base.
2. The perimeter of the base, \( P \), is \( 4s \).

Given:
- The length of the base \( s = 40 \) in.
- Surface area \( SA = 2800 \) in².

First, calculate the base area \( B \):
\[
B = s^2 = 40^2 = 1600 \text{ in}^2
\]

Now, calculate the perimeter \( P \):
\[
P = 4s = 4 \cdot 40 = 160 \text{ in}
\]

Now, substitute the values into the surface area formula:
\[
2800 = 1600 + \frac{1}{2} \cdot 160 \cdot l
\]

Subtract \( 1600 \) from both sides:
\[
2800 - 1600 = \frac{1}{2} \cdot 160 \cdot l
\]
\[
1200 = 80l
\]

Now, solve for \( l \):
\[
l = \frac{1200}{80} = 15 \text{ in}
\]

Therefore, the slant height \( l \) is **15 in**.