Question

The area of a triangle with sides 21cm, 20 cm and 13 cm is___ sq cm.

• A. 63
• B. 70
• C. 120
• D. 126

Answer 1

The correct option is D

126

The semi-perimeter (s) of a triangle with sides a, b and c is given by:
$s=\frac{a+b+c}{2}$
So, $s=\frac{21+20+13}{2}$

$⟹s=27$ cm
Then, the area of the triangle can be calculated using Heron's formula, given by:
Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$⟹\text{Area}=\sqrt{27(27-21)(27-20)(27-13)}$

$=\sqrt{27\left(6\right)\left(7\right)\left(14\right)}$

$=\sqrt{9\left(3\right)\left(6\right)\left(7\right)\left(7\right)\left(2\right)}$

$=\sqrt{3^2\times 6^2\times 7^2}$

$=3\times 6\times 7$

$=126\text{sq cm}$