Question

You have a triangular base with a base edge of 8 ft. and a base height of 4 ft.

The volume is 48 cu. ft. Find the height of the pyramid.

Answer 1

9 ft

Explanation:

The formula for calculating the volume of a triangular pyramid is:

V = ⅓Bℎ

where:

• V is the volume of the triangular pyramid;
• B is the area of the triangular base; and
• h is the height of the pyramid.

In your case, you have:

• B = ½ ⋅ 8 ⋅ 4 = 16 ft²(the area of a right triangle is half the product of its base and height);
• h is unknown; and
• V=48 ft³

Plugging these values into the formula, we get:

48 = ⅓ ⋅ 16 ⋅ ℎ

Solving for ℎ we get:

ℎ = (48 ⋅ 3/16) = 9 ft

Answer 2

The length is 4.5ft.

The formula and work are shown below