Question

1. find the surface area of the square pyramid

Explanation:

Step1: Calculate the area of the square base

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 12\) cm, so \(A_{base}=12\times12 = 144\) \(cm^{2}\).

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, the base \(b = 12\) cm and the height \(h = 10\) cm. So \(A_{triangle}=\frac{1}{2}\times12\times10=60\) \(cm^{2}\).

Step3: Calculate the total area of the four triangular faces

Since there are 4 triangular faces, \(A_{triangles}=4\times A_{triangle}\). Substituting the value of \(A_{triangle}\), we get \(A_{triangles}=4\times60 = 240\) \(cm^{2}\).

Step4: Calculate the surface area of the square pyramid

The surface area \(A\) of the square pyramid is the sum of the area of the base and the area of the four triangular faces. So \(A=A_{base}+A_{triangles}\). Substituting the values of \(A_{base}\) and \(A_{triangles}\), we have \(A = 144+240=384\) \(cm^{2}\).

Answer:

The surface area of the square pyramid is \(384\) \(cm^{2}\).