Question

Charles begins finding the volume of a trapezoidal prism using the formula a = one-half(b1 b2)h to find the prism's base area. a = ((x 4) (x 2))x a = (2x 6)x a = (x 3)x a = x2 3x 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. which expression can be used to represent the volume of the trapezoidal prism? 2x3 6x2 x3 6x2 x3 3x2 2x3 3x2

Answer 1

The volume of the trapezoidal prism having side lengths x, (x+2), (x+4) and height of 2x is 2x³+6x² option first is correct.

What is volume?

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of the trapezoidal prism can be given:

$\rm V=\frac{1}{2} (a+b)\times h \times L$

Where V = The volume of the trapezoidal prism:

Length of the trapezoid L = x

Top width  a = (x+2)

Base width  b = (x+4)

Height of the trapezoidal prism  h = 2x

$\rm V=\frac{1}{2} (x+2+x+4)\times 2x \times x$

$\rm V=\frac{1}{2} (2x+6)2x^2\\\\\rm V= (2x+6)x^2\\\\\rm V= (2x^3+6x^2)$

Thus, the volume of the trapezoidal prism is  $\rm (2x^3+6x^2)$

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