Question

1. find the surface area of the square pyramid

Explanation:

Step1: Calculate the area of the square base

The side length of the square base \(a = 12\) cm. The area of a square \(A_{base}=a^{2}\), so \(A_{base}=12\times12 = 144\) \(cm^{2}\).

Step2: Calculate the area of one triangular face

The base of each triangular face \(b = 12\) cm and the height of each triangular face \(h=10\) cm. The area of a triangle \(A_{triangle}=\frac{1}{2}\times b\times h\), so \(A_{triangle}=\frac{1}{2}\times12\times10=60\) \(cm^{2}\).

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) 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 pyramid

The surface area of the square - pyramid \(A=A_{base}+A_{triangles}\). Substituting the values of \(A_{base}\) and \(A_{triangles}\), we have \(A = 144+240\).

Answer:

\(384\) \(cm^{2}\)