Question

Mr. Buchanan is now homeless and wants to build a hollow equilateral trianglular pyramid to live in. What will the surface area of the pyramid be if its base side length is 28 in and its face height is 23 in?

Answer 1

`1644.96in^2`

Explanation:

The surface area of an equilateral triangular pyramid is given as:

`S = A + (3)/(2)bh`

where

`A = \sqrt{(3)/(4) }a^2` is the area of the pyramid's base

b = length of the base of one of the faces = 28 in

h = face height 23 in

The area of the base of the pyramid will be:

`A = \sqrt{(3)/(4) }a^2`
`= \sqrt{(3)/(4) } * 28^2`

`A = 678.96 in^2`

Hence:

`S = 678.96 + (3)/(2) * 28 * 23\\\\S = 678.96 + 966\\\\S = 1644.96in^2`

The surface area of the pyramid is
`1644.96in^2`