Question

find the surface area of this square pyramid. surface area of a pyramid la = 2bl sa = la + b 3 m 7 m sa = ? m²

Explanation:

Answer:

To find the surface area of the square pyramid, we use the formulas provided: \( LA = 2bl \) (lateral area) and \( SA = LA + B \) (surface area, where \( B \) is the area of the base).

1. Identify the values:

• The base is a square with side length \( b = 3 \, \text{m} \).
• The slant height \( l = 7 \, \text{m} \).

1. Calculate the lateral area (\( LA \)):

For a square pyramid, the lateral area formula \( LA = 2bl \) (or equivalently, \( 4 \times \frac{1}{2}bl \), since there are 4 triangular faces) gives:
\[
LA = 2 \times 3 \times 7 = 42 \, \text{m}^2
\]

1. Calculate the base area (\( B \)):

The base is a square, so \( B = b^2 \):
\[
B = 3^2 = 9 \, \text{m}^2
\]

1. Calculate the surface area (\( SA \)):

Using \( SA = LA + B \):
\[
SA = 42 + 9 = 51 \, \text{m}^2
\]

\( \boldsymbol{51} \)