Question

Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.

 

Answer 1

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

${\displaystyle A=\sqrt{s(s-a)(s-b)(s-c)}}$, where

${\displaystyle s=\frac{a+b+c}{2}}$
Therefore the area of a triangle, say having sides 3 cm, 4 cm and 5 cm is given by

a = 3 cm ; b = 4 cm ; c = 5 cm

${\displaystyle s=\frac{a+b+c}{2}}$

${\displaystyle s=\frac{3+4+5}{2}}$

${\displaystyle s=\frac{12}{2}}$

s = 6 cm Now, area ${\displaystyle A=\sqrt{s(s-a)(s-b)(s-c)}}$

$$=\sqrt{6(6-3)(6-4)(6-5)}$$
$$=\sqrt{6\times 3\times 2\times 1}$$
$$=\sqrt{36}$$
$$=6c{m}^2$$