Question

build your skills 10 find the total surface area of a square pyramid with a base of 12 cm by 12 cm, height of 8 cm.

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 12\space cm\). The area of a square is \(A_{base}=a^{2}\).

$$A_{base}=12^{2}=144\space cm^{2}$$

Step2: Calculate the area of one triangular face

The base of each triangular face is \(b = 12\space cm\) and the height of each triangular face is \(h = 8\space cm\). The area of a triangle is \(A_{triangle}=\frac{1}{2}\times b\times h\).

$$A_{triangle}=\frac{1}{2}\times12\times8 = 48\space cm^{2}$$

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=n\times A_{triangle}\)

$$A_{triangles}=4\times48=192\space cm^{2}$$

Step4: Calculate the total surface area

The total surface area \(A_{total}=A_{base}+A_{triangles}\)

$$A_{total}=144 + 192=336\space cm^{2}$$

Answer:

The total surface area of the square - pyramid is \(336\space cm^{2}\)