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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

Respuesta :

calculista

Answer:

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

Step-by-step explanation:

step 1

Find the area of the trapezoidal base

The area of a trapezoid is given by the formula

[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]

we have

[tex]b_1=(x+2)\ units\\b_2=(x+4)\\h=x[/tex]

substitute

[tex]A=\frac{1}{2}(x+2+x+4)x[/tex]

[tex]A=\frac{1}{2}(2x+6)x[/tex]

[tex]A=(x+3)x\\A=(x^2+3x)\ units^2[/tex]

step 2

Find the volume of the trapezoidal prism

we know that

The volume of the prim is given by

[tex]V=Bh[/tex]

where

B is the area of the base

H is the height of the prism

we have

[tex]B=(x^2+3x)\ units^2[/tex]

[tex]H=2x\ units[/tex]

substitute

[tex]V=(x^2+3x)2x\\V=(2x^3+6x^2)\ units^3[/tex]

therefore

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

[tex](2x^3+6x^2)[/tex]

Answer:

(A) - 2x3 + 6x2

Step-by-step explanation:

i got it right on edg 2020

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