Question

The volume of this right trapezoidal prism is 464.75 ft³.

What is the height, x, of the prism?

Enter your answer as a decimal in the box.

x = ft

Answer 1

Answer:

the answer is 14.3

Step-by-step explanation:

Answer 2

The height of the trapezoidal prism is 12.3 feet.

Formula for finding the volume of trapezoidal prism

$v = \frac{1}{2}(b_{1} +b_{2} )hl$

where,

v is the volume of trapezoidal prism

$b_{1}$ and $b_{2}$ are the bases

h is the height of trapezoidal prism

l is length of the trapezoidal prism

According to the given question

We have to find the value of x which is the length of trapezoidal prism.

And,

Volume, v = 464.75 cubic feet.

From the given figure

here,

$b_{1} = 5ft$, $b_{2} = 8ft$,  $h = xft$, and $l = 5.8ft$

Substitute all these values in the formula of the volume of trapezoidal prism

⇒ 464.75 = $\frac{1}{2}$ ×(5+8)(5.8)x

⇒929.5 = 13×5.8x

⇒$\frac{929.5}{(13)(5.8)}$ = $x$

⇒ x = 12.3 feet

Hence, the height of the 12.3 feet.

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