Question : The height of an equilateral triangle is $7 \sqrt{3}$ cm. What is the area of this equilateral triangle?
Option 1: $36 \sqrt{3}$ cm2
Option 2: $25 \sqrt{3}$ cm2
Option 3: $49 \sqrt{3}$ cm2
Option 4: $32 \sqrt{3}$ cm2
Correct Answer: $49 \sqrt{3}$ cm 2
Solution :
Height of an equilateral triangle = $\frac{\sqrt{3}}{2} \times Side$
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times Side^2$
So, each side of the triangle = $\frac{7\sqrt{3}}{\frac{\sqrt{3}}{2}}$ = 14 cm
Area of an equilateral triangle = $\frac{\sqrt{3}}{4} \times 14^2$ = $49\sqrt{3}$ cm
2
∴ The area of this equilateral triangle is $49\sqrt{3}$ cm
2
.
Hence, the correct answer is $49\sqrt{3}$ cm
2
.
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