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.

Answer 1

Answer:

(A) - 2x3 + 6x2

Step-by-step explanation:

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Answer 2

Answer:

The expression that can be used to represent the volume of the trapezoidal prism is  $(2x^3+6x^2)$

Step-by-step explanation:

step 1

Find the area of the trapezoidal base

The area of a trapezoid is given by the formula

$A=\frac{1}{2}(b_1+b_2)h$

we have

$b_1=(x+2)\ units\\b_2=(x+4)\\h=x$

substitute

$A=\frac{1}{2}(x+2+x+4)x$

$A=\frac{1}{2}(2x+6)x$

$A=(x+3)x\\A=(x^2+3x)\ units^2$

step 2

Find the volume of the trapezoidal prism

we know that

The volume of the prim is given by

$V=Bh$

where

B is the area of the base

H is the height of the prism

we have

$B=(x^2+3x)\ units^2$

$H=2x\ units$

substitute

$V=(x^2+3x)2x\\V=(2x^3+6x^2)\ units^3$

therefore

The expression that can be used to represent the volume of the trapezoidal prism is

$(2x^3+6x^2)$