What is the height of the trapezoidal base?

Question

volume= 628 cm cubed
height= 36 cm
lenghts of the two bases of the trapezoidal base are 20 cm and 28 cm...

What is the height of the trapezoidal base?

Answer 1

V = A x H

Since you know H = 36, then just divide that into 628. That tells you what A must be.

A = V / H
A = 628 / 36 = 17 4/9

So the area of the trapezoid is 17 4/9 cm².

For a trapezoid, the area is given by A = ½ h [b(1) + b(2)].

Letting 17 4/9 = A, then:

17 4/9 = ½ h (20 + 28)
17 4/9 = 24 h
(157 / 9) / 24 = h
157 /216 = h
0.72685 cm ≈ h

So the height of the trapezoid is approximately 0.72685 cm.

To verify, just plug the values back into the appropriate equations and multiply them all out. I have already done it, and they work.