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s344n2d4d5 [400]
1 year ago
15

A regular pentagonal prism has a volume of 2,850 cubic millimeters. what is the height of the prism? a regular pentagonal prism

with height labeled h. the pentagonal base has side edge labeled 12 millimeters. apothem from center to a base edge is labeled 5 millimeters. the height of the prism is millimeters.
Mathematics
1 answer:
zlopas [31]1 year ago
5 0

Answer:

Height = 19mm.

Step-by-step explanation:

Area of a regular polygon =  (A * P) / 2 where A = side / (2 * Tan (π / N)) where, N = Number of sides, A = Apothem,  P = Perimeter.

Here A = 5, P = 5*12 = 60 so

Area  of the base  = (5 * 60) / 2 = 150 mm^2.

Volume = area base * height so

Height = volume / area of base

            = 2850 / 150

            = 19 mm.

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