Question

A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters. Which expression represents the volume of the prism, in cubic centimeters? 9x2 + 7x 14x2 + 7x 16x2 + 14x 28x2 + 14x

Answer 1

Recall that the volume of a regular prism is given by the area of the base times the height.

Given that the base of the prism is a regular pentagon with an apothem of 2.8 centimeters.
The pentagon consist of 5 isosceles triangles with the apothem as the height and the side of the pentagon as the base.

Recall that the are of a triangle is given by 1/2 base times height.

Thus the area of of the pentagon base of the prism is given by
$Area= \frac{5}{2} x\times2.8=7x$

Therefore, the volume of the prism is given by
$Volume=7x(2x+1)=14x^2+7x$

Answer 2

The expression that represents the volume of the prism is $14x^2 + 7x$

The given parameters are:

• Apothem (a) = 2.8 cm
• Shape: Pentagon

Start, by calculating the area of the base of the prism using:

$A = \frac 12 aln$

Where:

• n, represents the number of sides (n = 5)
• l, represents the length of each side (l = x)

So, we have:

$A = \frac 12 \times 2.8 \times x \times 5$

$A = 7x$

The volume of the prism is then calculated as:

$V = Ah$

Where:

$h =2x + 1$

So, we have:

$A =7x \times (2x + 1)$

Expand

$A =14x^2 + 7x$

Hence, the expression that represents the volume of the prism is $14x^2 + 7x$

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