Question

find the surface area of the square pyramid: 8 cm 5 cm

Explanation:

Step1: Calculate 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, $B = 5^{2}=25$ $cm^{2}$.

Step2: Calculate area of one triangular face

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

Step3: Calculate total area of triangular faces

A square - pyramid has 4 triangular faces. The total area of the triangular faces $A_{triangles}=4\times A_{\triangle}$. So, $A_{triangles}=4\times20 = 80$ $cm^{2}$.

Step4: Calculate surface area

The surface area $SA$ of a square - pyramid is the sum of the base area and the total area of the triangular faces. So, $SA=B + A_{triangles}=25+80 = 105$ $cm^{2}$.

Answer:

$105$ $cm^{2}$