You need to use the volume equation of triangular prism, such that:
`V = A*h`
`A` represents the area of equilateral triangle that represents the base of prism
`h` represents the height of the prism
You need to evaluate the area of equilateral triangle such that:
`A = (l*l*sin 60^o)/2 => A = l^2*sqrt3/4`
The problem provides the information that the volume of the prism is of `100 cm^3` and the height of prism is of `10 cm` , such that:
`100 = ( l^2*sqrt3/4)*10 => 10 = l^2*sqrt3/4`
`40 = l^2*sqrt3 => l^2 = 40/sqrt 3 => l = sqrt((40sqrt3)/3)`
Hence, evaluating the length of side of equilateral triangle yields `l = sqrt((40sqrt3)/3).`
You need to remember the volume of the triangular prism:
V = Area of the base*height.
The area of the base =
l denotes the length of the side of equilateral triangle and the angle included is of .
Area of the base =
The length of the height of the prism is of 10 cm and the volume is of .
Replacing these values in the formula of volume yields:
l 4.805 cm
The length of the side of the equilateral base is about l 4.805 cm.