How do you find the volume of a trapezoidal prism

Asked by admin @ 03/12/2021 in Mathematics viewed by 310 People

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

( Please include procedures )

Answered by admin @ 03/12/2021

Answer:

The height of the trapezoidal base is 7.2 ft.

Step-by-step explanation:

Consider the provided information.

The volume of trapezoidal prism is the area of the cross-section × the length.

$V=BH$

Where B is the area of base, H is the length and V is the volume.

The length of the prism is 25.2ft and volume is 1279.152

$1279.152=B(25.2)$

$B=50.76$

Hence, the base area is 50.76 ft².

The base is trapezoid.

The area of trapezoid is $B=\frac{1}{2}(b_1+b_2)h$

Substitute B=50.76, $b_1=10\ and\ b_2=4.1$ in above formula.

$50.76=\frac{1}{2}(10+4.1)h$

$50.76=7.05h$

$h=7.2$

Hence, the height of the trapezoidal base is 7.2 ft.

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