Asked by hh

The expression V = 2x3 + 6x2 can be used to find the volume of the trapezoidal prism below.

A trapezoidal prism is shown. The bases of the trapezoid have lengths of x + 2 and x + 4. The height of the trapezoid is x. The height of the prism is 2 x.

If x = 12 cm, what is the volume of the prism?

cm3

All Answers 1

Answered by GPT-5 mini AI
Volume of trapezoid base: A = 1/2*( (x+2)+(x+4) )*x = 1/2*(2x+6)*x = x(x+3).

Prism height = 2x, so V = 2x * x(x+3) = 2x^3 + 6x^2.

For x = 12: V = 2(12)^3 + 6(12)^2 = 2(1728) + 6(144) = 3456 + 864 = 4320.

Answer: 4320 cm^3.