# A triangular prism of length 10 cm has a volume of 100 cm^3. If the base is an equilateral triangle, find it's length of side.

### 3 Answers | Add Yours

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.**

Area of an equilateral triangle with side a is [(sqrt3)a^2]/4.

The volume of prism with base area A and height h =base area*height. Height (or length) is given = 10cm

Therefore, the volume, v={[ (sqrt3)a^2]/4 }10 which is equal to 100cm^3.Solve for a from this equality.

(sqrt3)a^2 = 100*4/10.

a^2= sqrt(10*4/sqrt3)=sqrt(40/(sqrt(3) )= =**4.8056 cm** approximately.

Threfore, the length of the sides of the equilateral triangle is 4.8056cm approximately.

length of its side is 4.472.the formula used is 0.5xbhl