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? (2x + 1) 9x²+7x 14x² + 7x 16x² + 14x 28x² + 14x

Explanation:

Step1: Find the area of the base

The formula for the area of a regular polygon is $A = \frac{1}{2}aP$, where $a$ is the apothem and $P$ is the perimeter. For a regular pentagon with side - length $x$, the perimeter $P = 5x$. Given $a = 2.8$, the area of one pentagonal base $A_{base}=\frac{1}{2}\times2.8\times5x=7x$.

Step2: Calculate the volume of the prism

The volume of a prism is given by $V=A_{base}\times h$, where $h$ is the height of the prism. Here, the height of the prism $h=(2x + 1)$. So $V=7x\times(2x + 1)$.

Step3: Expand the expression

Using the distributive property $a(b + c)=ab+ac$, we have $V=7x\times2x+7x\times1=14x^{2}+7x$.

Answer:

$14x^{2}+7x$