Question

Find the area of the triangle having three sides given as $5cm,6cm$ and $7cm$.

• A. $6\sqrt{6}$ $c{m}^2$
• B. $6\sqrt{3}$ $c{m}^2$
• C. $4\sqrt{6}$ $c{m}^2$
• D. None of the above

Answer 1

The correct option is A $6\sqrt{6}$ $c{m}^2$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$ where, $s=\frac{a+b+c}{2}$

For triangle with sides 5 cm, 6 cm and 7 cm, $s=\frac{5+6+7}{2}=9cm$
Area of the triangle$=\sqrt{9(9-5)(9-6)(9-7)}=\sqrt{9\times 4\times 3\times 2}=6\sqrt{6}{cm}^2$