Question

The area of a triangle whose sides are $4cm,13cm$ and $15cm$, is

• A. $\sqrt{420}{cm}^2$
• B. $24{cm}^2$
• C. $48{cm}^2$
• D. $56{cm}^2$

Answer 1

The correct option is B $24{cm}^2$

The sides of triangle are $4cm,13cm,15cm$
Using Heron's formula,
Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$
where $s=\frac{a+b+c}{2}$
$\therefore s=\frac{4+13+15}{2}=16cm$
$\therefore$ Area $=\sqrt{16(16-4)(16-13)(16-15)}$
$\therefore$ Area $=\sqrt{16\times 12\times 3\times 1}$

$=4\times 6$
$=24{cm}^2$

Hence, option B.