Question

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Answer 1

h = 19 mm

Explanation:

the volume (V) of the prism is calculated as

V = Ah ( A is the area of the base and h the height )

the base is a regular pentagon whose area (A) is calculated as

A =
`(1)/(2)` pa ( p is the perimeter and a the apothem )

p = 5 × 12 = 60 mm and a = 5 mm , then

A =
`(1)/(2)` × 60 × 5 = 30 × 5 = 150 mm²

given V = 2850 , then

150h = 2850 ( divide both sides by 150 )

h = 19 mm