Question

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

Answer 1

Answer:

Option 4. Perimeter = 30 units

Step-by-step explanation:

Since the volume of a pentagonal prism is 840 cubic units.

Perpendicular distance between the bases = 14 units

We know volume of a pentagonal prism = Area of base × distance between the bases

840 = Area × 14

Area = 840/14 = 60 square units

Now area of a pentagon

$A=\frac{a^{2}}{4}\times\sqrt{5(5+2\sqrt{5})}$

$1.72a^{2}=60$

$a^{2}=\frac{60}{1.72}=34.90$

$a=\sqrt{34.9}=5.91$

Therefore perimeter of the pentagon = 5×a = 5×5.91 = 29.54 ≈ 30 units