Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm

Explanation

Let the sides of the triangle be `a, b` and `c`
Given length of the sides of the triangle are :-
`a = 8cm`
`b = 11cm`
`c = ?`
Perimeter of the triangle is `= 32cm`
Since the sum of all three sides of a triangle is it's perimeter
`=> a + b + c = 32cm`
`=> 8 + 11 + c = 32cm`
`=> 19 + c = 32cm`
`=> c = 32 - 19`
`=> c = 13cm`
Now we will find the area of the triangle by heron's formula which is `sqrt((s(s-a)(s-b)(s-c))` where s is the semi-perimeter of the triangle.
semi-perimeter of this triangle `= 32/2= 16cm`
Area of the triangle `= sqrt(16(16-8)(16-11)(16-13))`
`= sqrt(16 xx 8 xx 5 xx 3))`
`= sqrt(2 xx 2 xx 2 xx2 xx 2 xx 2 xx 2 xx 5 xx 3)`
`= 2 xx 2 xx 2 sqrt(2 xx 5 xx 3))`
`= 8 sqrt(30)cm^2`