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?

Answer 1

The expression representing the volume of the prism is given as:
Volume=[base area]*[height]
base area is the area of the pentagon;
The area of pentagon is given by:
Area of pentagon=a^2ntan(180/n)
a=apothem length
n=number of sides
Area=2.8^2*5tan(180/5)
Area=28.48=28.5 cm^2
Therefore the expression for the volume of the prism with height,h, will be:
volume=28.5h cm^3