Question

"Identify the volume of a regular triangular pyramid with base edge length 9 ft and height 12 ft. Round to the nearest tenth, if necessary."

I keep on getting 108 ft., but isn't the correct answer.

Answer 1

The area of any pyramid is the base area multiplied by the height and divided by three.

The base of a regular triangular pyramid is an equilateral triangle. The formula for the area of an equilateral triangle is
`(s^2√(3))/(4)`, where s is the side-length, so in this case, the base area is
`(81√(3))/(4)`. Now, we multiply by 12, the height, and divide by three (which is equivalent to multiplying by four overall), for a result of
`81√(3)`. To round to the nearest tenth, you'd generally need a calculator - using one, the answer is 140.3.