Question

find the surface area of the square - based pyramid. sa =? ft²

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 9\) ft. The area of a square is \(A_{base}=a^{2}\).

$$A_{base}=9^{2}=81$$

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 \(b = 9\) ft and the height (slant height) \(h = 15\) ft.

$$A_{\triangle}=\frac{1}{2}\times9\times15=\frac{135}{2} = 67.5$$

Step3: Calculate the total area of the four triangular faces

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

$$A_{triangles}=4\times67.5 = 270$$

Step4: Calculate the total surface area

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.

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

$$SA = 81+270$$

Answer:

\(351\)