Question

The right pengtagonal prism has a height of of 14 units. The volume of the prism is 840 cubic units. What is the perimeter of the base? 12 units 15 units 21 units 30 units

Answer 1

D is correct

Explanation:

just took the test on edg 2020

Answer 2

Option D is correct.

Explanation:

Height of prism = 14 units

Volume of prism = 840 cubic units

Perimeter of base = ?

Volume of Prism = Base Area * Height

840 = Base Area * 14

=>Base Area = 840/ 14

Base Area = 60 square unit.

Now Area of pentagon:

`Area=(a^2)/(4)\sqrt{5(5+2√(5)}`

We need to find a, where Area = 60

`60=(a^2)/(4)*6.88\\60=a^2*1.72\\=>a^2=60/1.72\\=>a^2=34.88\\=>a=√(34.88)\\ a=5.91`

The pentagon has 5 sides.

So, perimeter of base = 5*a

perimeter of base = 5* 5.91

perimeter of base = 29.55 ≈ 30 units

So, Option D is correct.