Question

What is the area of a triangle formula given 3 sides?

Answer 1

Herons formulae

RT S(S-A)(S-B)(S-C)

Answer 2

The formula is called Heron’s Formula. It is the method of calculating the area of a triangle when its 3 sides are given. To use Heron’s formula with given sides a, b and c  

s = $\frac{a +b+c}{2}$  

where s is the semiperimeter  

Area = $\sqrt{s(s-a)(s-b)(s-c)}$  

For example, consider a triangle whose sides are 3 cm, 5 cm and 2 cm. To find the area:

A=4×$\frac 32$=6  

Using Heron's formula  

s = $\frac{3+4+5}{2}$ =6  

And, A= $\sqrt{6*(6-5)*(6-4)*(6-3)}$  

           = 6