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:Option D is correct.Step-by-step explanation:Height of prism = 14 unitsVolume of prism = 840 cubic unitsPerimeter of base = ?Volume of Prism = Base Area * Height840 = Base Area * 14=>Base Area = 840/ 14Base Area = 60 square unit.Now Area of pentagon:[tex]Area=\frac{a^2}{4}\sqrt{5(5+2\sqrt{5}}[/tex]We need to find a, where Area = 60[tex]60=\frac{a^2}{4}*6.88\\60=a^2*1.72\\=>a^2=60/1.72\\=>a^2=34.88\\=>a=\sqrt{34.88}\\ a=5.91[/tex]The pentagon has 5 sides.So, perimeter of base = 5*aperimeter of base = 5* 5.91perimeter of base = 29.55 ≈ 30 unitsSo, Option D is correct.