Question

A backpacking tent in the shape of a triangular prism has sides that are 6 ft and a length of 7 ft. What is the volume of the tent to the nearest whole number?

Answer 1

volume of an equilateral triangle with sides equal to 6 is 9sqrt(3)

volume of tent is 63sqrt(3) = 109.119 is about 109 ft^3

Answer 2

Volume of the tent is 109 cubic feet.

Explanation:

Volume of a triangular prism = Area of triangular base × Height

In the question triangular base is an equilateral triangle with a side = 6 ft

Height of the prism = 7 ft.

Now area of the triangular base = (1/2)×Base×height = (1/2)×[√(36-9)]×6

Area = (1/2)×6×√27 = 3×3√3 = 9√3 square feet

Now volume of the prism = (9√3) × 7 = 63√3 = 63×1.732 =109.12 cubic feet.

Therefore volume of the tent is 109 cubic feet.