Chapter 12.2, Problem 6PSB

To determine

To calculate: The total area of regular pyramid.

Answer to Problem 6PSB

The total area of regular pyramid is $105$ .

Explanation of Solution

Given information:

Side PK =8.

The area of square base is 25.

Formula used:

Area of triangle: $A=\frac{1}{2}\times b\times h$

b = base of triangle

h = height of triangle Area of square: $A=s^2$

s = side of square

Calculation:

  

If the square base is 25,

  $\begin{array}{l}25=s^2\\ s=\sqrt{25}\\ s=5\end{array}$

AB = s = 5

There are four triangles.

Lateral Area = 4 $\times$ Area of triangle

Lateral Area $=4\times \frac{1}{2}\times AB\times PK$

Lateral Area $=4\times \frac{1}{2}\times 5\times 8$

Lateral Area $=80$

Total Area = Lateral Area + Area of base

Total Area $=80+25=105$