Jeylen C.

asked • 05/09/20# find the height of the triangular pyramid when the volume is 318 square centimeters.

## 2 Answers By Expert Tutors

Need to assume that the pyramid is regular (all sides equal), otherwise there are many answers possible, depending on the area of the base.

Here is an outline of the process:

Let the length of a side be x.

Find the area of an equilateral triangle with side x. This is the base of the pyramid

Then consider a right triangle that consists of the apex of the pyramid, one of the corner vertices of the base, and the center of the base. It is a right triangle "by symmetry". You can also use the fact that the distance of the center of the base to a vertex of an equilateral triangle is 2/3 of the length of the median (which for an equilateral triangle is also an altitude). So the height is the missing side of a right triangle whose hypotenuse is x, and whose other side is 2/3 x.

Once you have the expression for the height in terms of x, use that expressions for the height, and the expression for area of the base, and the formula for the Volume V of a pyramid, V = 1/3 base * height.

This will give you an equation with 318 = 1/3 (base in terms of x) * (height in terms of x)

Solving this equation will determine x, the length of the side of the pyramid.

Finally, use your equation for the height in terms of x, to determine the height, now that x is known.

volume=bh/3=318cu/ft

Not enough imfo.

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Douglas B.

05/09/20