Question

solve surface area for square pyramid with side of 15 and slant height of 9.9

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces. The formula for the surface area \( S \) of a square pyramid with base side \( a \) and slant height \( l \) is given by:

\[
S = a^2 + 2 \cdot a \cdot l
\]

where:
- \( a \) is the length of one side of the square base.
- \( l \) is the slant height.

Given:
- \( a = 15 \)
- \( l = 9.9 \)

Now, we can calculate the surface area:

1. Calculate the area of the base:
\[
a^2 = 15^2 = 225
\]

2. Calculate the area of the four triangular faces:
\[
2 \cdot a \cdot l = 2 \cdot 15 \cdot 9.9 = 2 \cdot 15 \cdot 9.9 = 297
\]

3. Combine both areas to find the total surface area:
\[
S = 225 + 297 = 522
\]

Thus, the surface area of the square pyramid is \( 522 \) square units.