Question

find the surface area of the square - based pyramid. sa =? in²

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(s = 8\) in. The area of a square is \(A_{base}=s^{2}\).

$$A_{base}=8^{2}=64$$

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A_{\triangle}=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(b = 8\) in and the height (slant height) \(h = 12\) in.

$$A_{\triangle}=\frac{1}{2}\times8\times12=48$$

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=4\times A_{\triangle}\)

$$A_{triangles}=4\times48 = 192$$

Step4: Calculate the surface area of the pyramid

The surface area \(SA\) of the square - based pyramid is the sum of the area of the base and the area of the four triangular faces.

$$SA=A_{base}+A_{triangles}$$

$$SA = 64+192$$

Answer:

\(256\)