Question

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

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

Answer 1

The correct option is B $24c{m}^2$

Let $a=4$ cm, $b=13$ cm, $c=15$ cm

Semiperimeter $s=\frac{4+15+13}{2}\Rightarrow 16$

Area of $△=\sqrt{s(s-a)(s-b)(s-c)}$

Area of $△=\sqrt{16(16-4)(16-13)(16-15)}$

Area of $△=\sqrt{16\times 12\times 3\times 1}$

Area of $△=\sqrt{576}$

Area of $△=24c{m}^2.$