The right pentagonal prism has a height of 14 units. The volume of the prism is 840 cubic units. What is the perimeter of the base?

Solution:

Given, volume of the prism = 840 cubic units.

Height = 14 units

We have to find the perimeter of the base.

Volume of the prism = base area × height

840 = base area × 14

Base area = 840/14

Base area = 60 square units.

Area of pentagon = \(\frac{a^{2}}{4}\sqrt{5(5+2\sqrt{5})}\)

60 = (a²/4) × 6.88

a² = 240/6.88

a² = 34.88

Taking square root,

a = 5.91

Perimeter of pentagon = 5a

= 5(5.91)

= 29.55 ≈ 30

Therefore, the perimeter of the base is 30 units.

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The right pentagonal prism has a height of 14 units. The volume of the prism is 840 cubic units. What is the perimeter of the base?

Summary:

The right pentagonal prism has a height of 14 units. The volume of the prism is 840 cubic units. The perimeter of the base is 30 units.