Question

Find the lateral surface area and volume of the object shown in picture

Answer 1

The given figure is a triangular base pyramid. The formula for determining the lateral surface area of a triangular pyramid is expressed as

Lateral surface area = 1/2(perimeter of the base x slant height)

Recall, perimeter of a triangle is the sum of the sides of the triangle

Since the base of the given pyramid is equilateral, it means that all the sides are equal. Thus,

perimeter of base = 12 + 12 + 12 = 36

slant height = 10.6

Thus,

Lateral surface area = 1/2(36 x 10.6) = 190.8

The formula for determining the volume of a triangular pyramid is expressed as

Volume = 1/3 x base area x height

The formula for finding the base area of an equilateral triangle is expressed as

`\begin{gathered} \text{Area = a}^3*\sqrt[]{2}\text{ / 12} \\ \text{where a is the length of each side} \\ \text{Volume = 12}^3*\frac{\sqrt[]{2}}{12}\text{ = 203.65} \end{gathered}`