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.

P.S: I think it's 14.3ft since I did the math for it.

Answer 1

14.3 ft

Explanation:

To solve for the height of the right trapezoidal prism, we need to use the formula for the volume of a trapezoidal prism:

V = Area of trapezoid* height

=(1/2)h(b1 + b2)*x

Where:

V is the volume of the prism

h is the height of the trapezoid

b1 and b2 are the lengths of the parallel sides of the trapezoid

x is the height of the prism

From the problem, we know that the volume of the prism is 464.75 ft³. We also know that the prism is right, which means that one of the angles of the trapezoid is a right angle.

We can set up an equation using the formula above and the given measurements:

464.75 = (1/2)*5*(5+8)*x

Simplifying the equation, we get:

464.75= 32.5 x

x=464.75/32.5

x=14.3 ft

Therefore, the height of the prism is14.3