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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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