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

illusiia

illusiia

Answered question

2021-03-07

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

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-03-08Added 117 answers

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: 1279.152=B(25.2)
B=(1279.152/25.2)

B=50.76ft2

B is the area of the trapezoid base. The area of a trapezoid is given by: A=1/2(b1+b2) height
where b1 and b2 are the base lengths and h is the height. So, we have: 50.76=1/2(4.1+10)h
50.76=1/2(14.1)h
50.76=7.05h

h=50.76/7.05

h=7.2ft

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