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 2800 in square

Answer 1

The surface area \( SA \) of a square pyramid can be calculated using the formula:

\[
SA = b^2 + 2bs
\]

where:
- \( b \) is the length of the base,
- \( s \) is the slant height.

Given:
- \( b = 40 \) inches,
- \( SA = 2800 \) square inches.

First, we can calculate \( b^2 \):

\[
b^2 = 40^2 = 1600 \text{ square inches}
\]

Now we can substitute \( b \) and \( SA \) into the surface area formula:

\[
2800 = 1600 + 2(40)s
\]

Simplifying this, we have:

\[
2800 = 1600 + 80s
\]

Now, subtract \( 1600 \) from both sides:

\[
2800 - 1600 = 80s
\]
\[
1200 = 80s
\]

Next, divide both sides by \( 80 \) to solve for \( s \):

\[
s = \frac{1200}{80} = 15 \text{ inches}
\]

Thus, the slant height \( s \) is:

\[
\boxed{15} \text{ inches}
\]