# Prisms

The solid prism has constant cross section which is a trianle sides 8cm, 7cm and 7cm long respectively. If the lenght of the prism is 9cm, calculate the volume of the prism.

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1. Recall that the area of a prism is just area of the base times height. In this case, the base is the triangle. Since the lengths of side of triangle are given, we use Heron's formula to get first the area:
A = √(s(s-a)(s-b)(s-c))
where
a, b & c = lengths of side of triangle
s = half of the perimeter = 1/2*(a+b+c)
Substituting,
s = 1/2*(7+7+8)
s = 1/2*(22)
s = 11
A = √(s(s-a)(s-b)(s-c))
A = √(11(11-7)(11-7)(11-8))
A = √(11(4)(4)(3))
A = √(528)
A = 4√(33) = 22.98 cm^2

Finally, we multiply this to the height of the cylinder to get the volume:
V = A*h
V = 22.98*9
V = 206.8 cm^3

Hope this helps~ :)

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posted by Jai

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