Area of an equilateral triangle of side x is

A) \( \Large \frac{x^{2}}{\sqrt{2}} \)

B) \( \Large \frac{\sqrt{3}}{4} x^{2} \)

C) \( \Large \frac{\sqrt{3}}{2} x^{2} \)

D) \( \Large \frac{\sqrt{3}}{2} x^{3} \)

Correct answer:
B) \( \Large \frac{\sqrt{3}}{4} x^{2} \)

Description for Correct answer:


\( \Large AD = \sqrt{AB^{2}-BD^{2}} \)

= \( \Large \sqrt{x^{2}-\frac{x^{2}}{4}} \)

= \( \Large \frac{\sqrt{3}}{2}x \)

Therefore, Area of \( \Large \triangle ABC = \frac{1}{2} \times BC \times AD \)

= \( \Large \frac{1}{2} \times x \times \frac{x\sqrt{3}}{2} \)

= \( \Large \frac{\sqrt{3}}{4}x^{2} \)


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