Question

In $△ABC,a=4cm,b=6cm\text{and}\angle C={30}^{\circ }$, then the area of the triangle is

• A. $12c{m}^2$
• B. $6\sqrt{2}c{m}^2$
• C. $\frac{12}{\sqrt{3}}c{m}^2$
• D. $6c{m}^2$

Answer 1

The correct option is D $6c{m}^2$

In triangle $△ABC$,
$a=4cm$
$b=6cm$
$\angle C={30}^{\circ }$

We know that,
Area of the triangle $=\frac{1}{2}ab\sin C$
$=\frac{1}{2}\times 4\times 6\times \sin {30}^{\circ }$
$=2\times 6\times \frac{1}{2}[\because \sin {30}^{\circ }=\frac{1}{2}]$
$=6c{m}^2$
Therefore, area of triangle is $6c{m}^2.$