Question

In $△ABC,AB=6cm,BC=7cm$ and $AC=5cm$. Find the area of $△ABC$

• A. $6\sqrt{6}c{m}^2$
• B. $6\sqrt{3}c{m}^2$
• C. $6\sqrt{2}c{m}^2$
• D. $9\sqrt{6}c{m}^2$

Answer 1

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

Using Heron's formula,

Area of a triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

where $s=$ semiperimeterof the triangle

$a=$ length of side $BC$

$b=$ length of side $AC$

$c=$ length of side $AB$

In $△ABC,a=7,b=5,c=6$

Semiperemeter of $△ABC=s=\frac{a+b+c}{2}$

$=\frac{7+5+6}{2}$

$=9$

Hence, the area of $△ABC=\sqrt{9\times (9-7)\times (9-5)\times (9-6)}$

$=\sqrt{9\times 3\times 2\times 4}$

$=6\sqrt{6}c{m}^2$