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
Answer: 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.