Question

find the surface area of the square pyramid shown below. 6 yd 10 yd 10 yd

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(10\) yd.
The area of a square is \(A_{base}=s^2\), where \(s = 10\) yd.
So, \(A_{base}=10\times10=100\) \(yd^{2}\).

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 each triangular face is \(10\) yd (the side of the square base) and the height (slant height) is \(6\) yd.
So, \(A_{\triangle}=\frac{1}{2}\times10\times6 = 30\) \(yd^{2}\).

Step3: Calculate the total area of the four triangular faces

Since there are \(4\) triangular faces, \(A_{triangles}=4\times A_{\triangle}\).
\(A_{triangles}=4\times30 = 120\) \(yd^{2}\).

Step4: Calculate the total surface area

The total surface area \(A\) of the square - pyramid is the sum of the area of the base and the area of the four triangular faces.
\(A=A_{base}+A_{triangles}\).
\(A = 100+120\).

Answer:

\(220\) \(yd^{2}\)