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 given = `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 × 8 × 5 × 3)]`
= `sqrt [(2×2×2×2×2×2×2 × 5 × 3)]`
=`(2×2×2 ) sqrt[(2 × 5 × 3)]`
=` 8√30 sq cm`.