Answer:
h = 19 mm
Step-by-step 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 = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
p = 5 × 12 = 60 mm and a = 5 mm , then
A = [tex]\frac{1}{2}[/tex] × 60 × 5 = 30 × 5 = 150 mm²
given V = 2850 , then
150h = 2850 ( divide both sides by 150 )
h = 19 mm
