Question

Find the lateral area for the pyramid with the equilateral base

A: 144 sq. units
B: 180 sq. units
C: 288 sq. units

Answer 1

The lateral area for the pyramid with the equilateral base is 144 square units

Solution:

The given pyramid has 3 lateral triangular side

The figure is attached below

Base of triangle = 12 unit

Find the perpendicular

By Pythagoras theorem

`hypotenuse^2 = opposite^2 + adjacent^2`

Therefore,

`opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8`

Find the lateral surface area of 1 triangle

`\text{ Area of 1 lateral triangle } = (1)/(2) * opposite * base`

`\text{ Area of 1 lateral triangle } = (1)/(2) * 8 * 12\\\\\text{ Area of 1 lateral triangle } = 48`

Thus, lateral surface area of 3 triangle is:

3 x 48 = 144

Thus lateral area for the pyramid with the equilateral base is 144 square units