Question

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

• A. $576c{m}^2$
• B. $30c{m}^2$
• C. $26c{m}^2$
• D. $24c{m}^2$

Answer 1

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

$a=4cm$

$b=13cm$

$c=15cm$

Semiperimeter $\left(s\right)=\frac{a+b+c}{2}=\frac{4+13+15}{2}=16cm$

By Heron's formula,

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{16(16-4)(16-13)(16-15)}=\sqrt{16\times 12\times 3\times 1}=\sqrt{576}=24{cm}^2$