Question

find the surface area of a square pyramid with side length 3 yd and slant height 4 yd.

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 3\) yd. The area of the base \(B\) is \(B=s^{2}\).
\(B = 3^{2}=9\) yd².

Step2: Calculate the lateral surface area

The lateral surface area of a square - pyramid is \(LSA = 2sl\), where \(s\) is the side length of the base and \(l\) is the slant height. Here, \(s = 3\) yd and \(l = 4\) yd.
\(LSA=2\times3\times4=24\) yd².

Step3: Calculate the total surface area

The total surface area \(SA\) of a square - pyramid is \(SA=B + LSA\).
\(SA=9 + 24\).

Answer:

\(33\) yd²