Question

find the surface area of a square pyramid with side length 6 cm and slant height 5 cm.

Explanation:

Step1: Calculate the base area

The base is a square with side length \(a = 6\) cm. The area of the base \(B=a^{2}\), so \(B = 6\times6=36\space cm^{2}\)

Step2: Calculate the lateral surface area

The lateral surface area of a square pyramid is \(LSA=\frac{1}{2}\times perimeter\times slant\space height\). The perimeter of the base \(P = 4a\), with \(a = 6\) cm, so \(P=4\times6 = 24\) cm. The slant height \(l = 5\) cm. Then \(LSA=\frac{1}{2}\times24\times5=60\space cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(SA=B + LSA\). Substitute \(B = 36\) and \(LSA=60\) into the formula. So \(SA=36 + 60=96\space cm^{2}\)

Answer:

\(96\)