question_answer

Two vertices of an equilateral triangle are origin and (4, 0). What is the area of the triangle?

A) \[4\] sq units                  

B) \[\sqrt{3}\]sq units

C) \[4\sqrt{3}\] sq units       

D) \[2\sqrt{3}\] sq units

Correct Answer: C

Solution :

Since, triangle is equilateral.

\[\therefore \]\[AB=BC=CA\]\[\Rightarrow \]\[BD=\frac{4}{2}=2\]

In \[\Delta ADC,\]\[A{{D}^{2}}={{4}^{2}}-{{2}^{2}}=16-4=12\]

\[\Rightarrow \]   \[AD=2\sqrt{3}\]

\[\therefore \]Area of \[\Delta ABC=\frac{1}{2}\times BC\times AD=\frac{1}{2}\times 4\times 2\sqrt{3}\]

\[=4\sqrt{3}\,sq\text{ }units\]