Question

The side of trinagle 18cm 20cm and 22cm find its area

Answer 1

We can find the area of the triangle using Heron's formula as there is  height and base are specified 

Heron's formula : √ s (s -a) (s - b) (s -c)

Sides of the triangles:

a = 18 cm
b = 20 cm
c = 22 cm

Perimeter = 18 + 20 + 22 = 60
S = 60/ 2 = 30

s - a = 30 -  18 = 12
s - b = 30 - 20  = 10
s - c = 30 - 22 = 8

√ 30  (12) (10) (8)
= √  2 x 5 x 3 x 2 x 3 x 2 x 5 x 2 x 2 x 2 x2
= 2 x 3 x 5 x 2 x 2 x √2
=  120 √ 2 cm²

Answer 2

a=18 cm
b=20cm
c=22cm
By heron's formula,
Area=√s(s-a)(s-b)(s-c)
where s=a+b+c/2(perimeter)=60/2=30 cm
⇒√30(30-18)(30-20)(30-22)
⇒√30(12)(10)(8)
⇒√2^4*5^3*3^3
⇒√2^7*5^3*3^3*2
⇒√2^6*5^3*3^3
⇒2*2*3*5*2√2
⇒120√2 cm^3