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

Question
Solid Geometry
asked 2021-03-07
The volume of the trapezoidal prism is 1279.152 cubic feet. Determine the height of the trapezoid base.

Answers (1)

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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