Question

1. determine the surface area of the pyramid below. 10 cm 6 cm 6 cm

Explanation:

Step1: Calculate base area

The base is a square with side - length $a = 6$ cm. The area of the base $A_{base}=a^{2}=6^{2}=36$ $cm^{2}$.

Step2: Calculate area of one triangular face

The base of each triangular face is $b = 6$ cm and the height (slant - height) is $h = 10$ cm. The area of one triangular face $A_{triangle}=\frac{1}{2}bh=\frac{1}{2}\times6\times10 = 30$ $cm^{2}$.

Step3: Calculate total area of triangular faces

A square - based pyramid has 4 triangular faces. The total area of the triangular faces $A_{triangles}=4\times A_{triangle}=4\times30 = 120$ $cm^{2}$.

Step4: Calculate surface area

The surface area $A$ of the pyramid is the sum of the base area and the total area of the triangular faces. $A=A_{base}+A_{triangles}=36 + 120=156$ $cm^{2}$.

Answer:

$156$ $cm^{2}$