The sides of a triangle are 12 cm, 35 cm and 37 cm respectively. Find its area.

Given:

The sides of a triangle are 12 cm, 35 cm and 37 cm respectively. 

To do:

We have to find the area of the triangle.
Solution:

We can use heron's formula to find the area of the triangle:

Semi perimeter ( s)  $=\ \frac{a\ +\ b\ +\ c}{2}$

Semi perimeter ( s)  $=\ \frac{12\ +\ 35\ +\ 37}{2}$

Semi perimeter ( s) $=\ \frac{84}{2}$

Semi perimeter ( s) $=\ 42$

Now,

Area of triangle $=\ \sqrt{s( s\ -\ a)( s\ -\ b)( s\ -\ c)}$

Area of triangle $=\ \sqrt{42( 42\ -\ 12)( 42\ -\ 35)( 42\ -\ 37)} \ \ cm^{2}$

Area of triangle $=\ \sqrt{42( 30)( 7)( 5)} \ \ cm^{2}$

Area of triangle $=\ \sqrt{6\ \times \ 7\ \times \ 6\ \times \ 5\ \times \ 7\ \times \ 5} \ \ cm^{2}$

Area of triangle $=6\times7\times5\ cm^2$

Area of triangle $=210\ cm^2$

The area of the triangle is 210 cm$^2$.