Question

find the surface area of the square pyramid.

Explanation:

Step1: Find base area

The base is a square with side length $s = 5$ cm. The area of the base $B$ is given by $B=s^{2}$, so $B = 5^{2}=25$ cm².

Step2: Find area of one triangular face

The base of each triangular face is $b = 5$ cm and the height (slant - height) $l=8$ cm. The area of a triangle is $A_{\triangle}=\frac{1}{2}bl$. So $A_{\triangle}=\frac{1}{2}\times5\times8 = 20$ cm².

Step3: Find total area of 4 triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{\triangle}=4\times20 = 80$ cm².

Step4: Find surface area

The surface area $SA$ of the square - pyramid is the sum of the base area and the area of the 4 triangular faces. So $SA=B + A_{triangles}=25+80 = 105$ cm².

Answer:

105 cm²