The pentagonal prism has a perpendicular distance of 14 units between the bases. The volume of the prism is 840 cubic units. What is the perimeter of the base? 12 units 15 units 21 units 30 units

The answer is 30 units

To get the perimeter of the pentagonal base we proceed as follows;

volume of the prism = [base area]*[height]

base area (BA) = [volume]/[height]

volume=840

height=14

BA=840/14

BA=60 sq. units

Area of pentagon is given by:

Area=1/4sqrt (5 (5+2sqrt (5))) a^2

where a is the side length;

therefore to get the value of a we proceed as follows;

60=1/4sqrt (5 (5+2sqrt (5))) a^2

multiplying both sides by 4 we get:

240 = (5 (5+2sqrt (5))) a^2

but

(5 (5+2sqrt (5))) = 1.7205

thus;

240=1.7205a^2

dividing both sides by 1.7205 we get:

240/1.7205 = (1.7205a^2) / 1.7205

139.5=a^2

getting the square root of both sides we get:

sqrt (139.5) = sqrt (a^2)

11.8=a

thus a=11.8 units-=12 units (in 2 s. f)

the answer is 12 units