Question

The area of the $∆ABC$, in which $a=1,b=2,\angle C={60}^{\circ }$, is

• A. $4squnits$
• B. $\frac{1}{2}squnits$
• C. $\frac{\sqrt{3}}{2}squnits$
• D. $\sqrt{3}squnits$

Answer 1

The correct option is C

$\frac{\sqrt{3}}{2}squnits$

Explanation for correct option

Calculating the area of the triangle

Given, In $∆\mathrm{ABC}$, $a=1,b=2,\angle c={60}^{°}$

We know that, the area of the triangle is given by:

$$\begin{gathered} =\frac{1}{2}ab\sin c \\ =\frac{1}{2}\times \left(1\right)\times \left(2\right)\times \left(\sin 60°\right)\left[\because \sin 60=\frac{\sqrt{3}}{2}\right] \\ =\frac{\sqrt{3}}{2} \end{gathered}$$

Hence, the correct answer is Option (C).