Question

The volume of a triangular pyramid is 1,800 cubic inches. If the base of the solid has a height of 18 inches and a base of 12 inches, what is the height and area of the pyramid?

Answer 1

To find the height and area of the pyramid, we first need to find the height of the pyramid.

The formula for the volume of a triangular pyramid is:

Volume = (1/3) * base area * height

We are given that the volume is 1,800 cubic inches and the base area is 12 inches * 18 inches = 216 square inches. Plugging these values into the formula, we get:

1,800 = (1/3) * 216 * height
1,800 = 72 * height
height = 1,800 / 72
height = 25 inches

Now that we have found the height of the pyramid, we can find the area of the pyramid. The formula for the area of a triangular pyramid is:

Area = 1/2 * base perimeter * slant height

The base perimeter can be found by adding the lengths of the base sides:

Base perimeter = 12 + 12 + 18 = 42 inches

Using the Pythagorean theorem, we can find the slant height of the pyramid:

slant height = sqrt(18^2 + 12^2)
slant height = sqrt(324 + 144)
slant height = sqrt(468)
slant height = 21.63 inches

Plugging these values into the formula for the area of the pyramid, we get:

Area = 1/2 * 42 * 21.63
Area = 454.86 square inches

Therefore, the height of the pyramid is 25 inches and the area of the pyramid is 454.86 square inches.