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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


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 27th Jan, 2024

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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