The height of the trapezoidal prism is 12.3 feet.
Formula for finding the volume of trapezoidal prism
[tex]v = \frac{1}{2}(b_{1} +b_{2} )hl[/tex]
where,
v is the volume of trapezoidal prism
[tex]b_{1}[/tex] and [tex]b_{2}[/tex] 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,
[tex]b_{1} = 5ft[/tex], [tex]b_{2} = 8ft[/tex], [tex]h = xft[/tex], and [tex]l = 5.8ft[/tex]
Substitute all these values in the formula of the volume of trapezoidal prism
⇒ 464.75 = [tex]\frac{1}{2}[/tex] ×(5+8)(5.8)x
⇒929.5 = 13×5.8x
⇒[tex]\frac{929.5}{(13)(5.8)}[/tex] = [tex]x[/tex]
⇒ x = 12.3 feet
Hence, the height of the 12.3 feet.
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