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?

The question is missing the options and the the drawing of the prism. Here is the complete question and the drawing is in the attachment.

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?

a) 9x² + 7x

b) 14x² + 7x

c) 16x² + 14x

d) 28x² + 14x

b) 14x² + 7x

Step-by-step explanation: The formula to calculate the volume of a prism is:

V = Ab*h

Where

Ab is area of the base

h is the height of the prism

The base is a regular pentagon, which means that all the 5 sides of it is the same. The apothem of a pentagon is a line segment from the center of the pentagon to its side. The area is:

Ap =

where:

P is perimeter

a is apothem

Area of base:

Ab =

Ab =

Ab = 7x

h = 2x+1

Volume of the prism:

V = Ab.h

V = 7x.(2x+1)

V = 14x² + 7x

The expression that represents the volume of this prism is V = 14x² + 7x cubic inches.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240

4

step-by-step explanation: