Question

Find the area of the triangle whose sides are 18 m, 24 m and 30 m.

• A. $216m^2$
• B. $36m^2$
• C. $144m^2$
• D. $196m^2$

Answer 1

The correct option is A

$216m^2$

The semi-perimeter (s) of a triangle with sides a, b and c is given by:
$s=\frac{a+b+c}{2}$
So, $s=\frac{18+24+30}{2}$
$⟹s=36$ m
Then, the area of the triangle can be calculated using Heron's formula, given by:
Area $=\sqrt{s(s-a)(s-b)(s-c)}$
$⟹\text{Area}=\sqrt{36(36-18)(36-24)(36-30)}$
$=\sqrt{36\times 18\times 12\times 6}$

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

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

$=6\times 6\times 3\times 2$

$=216\text{sq m}$