# The volume of the trapezoidal prism is 1279.152 cubic feet. Determine the height of the trapezoid base.

Question
Solid Geometry
The volume of the trapezoidal prism is 1279.152 cubic feet. Determine the height of the trapezoid base.

2021-03-08
The volume of a prism is the product of the base B and its height H: V=BH
We are given that V=1279.152 cubic feet and H=25.2 ft so we can solve for B: $$\displaystyle{1279.152}={B}{\left({25.2}\right)}$$
B=(1279.152/25.2)ZSK
B=50.76ft^2ZSK
B is the area of the trapezoid base. The area of a trapezoid is given by: A=1/2(b1+b2)ZSKheight
where b1 and b2 are the base lengths and h is the height. So, we have: 50.76=1/2(4.1+10)hZSK
50.76=1/2(14.1)hZSK
50.76=7.05hZSK
h=50.76/7.05ZSK
h=7.2ft

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