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
[tex]A=\frac{a^{2}}{4}\times\sqrt{5(5+2\sqrt{5})}[/tex]
[tex]1.72a^{2}=60[/tex]
[tex]a^{2}=\frac{60}{1.72}=34.90[/tex]
[tex]a=\sqrt{34.9}=5.91[/tex]
Therefore perimeter of the pentagon = 5×a = 5×5.91 = 29.54 ≈ 30 units
