Question : The height of an equilateral triangle is 18 cm. Its area is:
Option 1: $36\sqrt{3}\operatorname{cm^2}$
Option 2: $108\sqrt{3}\operatorname{cm^2}$
Option 3: $108\operatorname{cm^2}$
Option 4: $96\sqrt{3}\operatorname{ cm^2}$
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Correct Answer: $108\sqrt{3}\operatorname{cm^2}$
Solution : Given that the height ($h$) of the equilateral triangle is 18 cm. $ h = \frac{\sqrt{3}}{2} \times a $ $ a = \frac{2h}{\sqrt{3}} = \frac{2 \times 18}{\sqrt{3}} = 12\sqrt{3}\operatorname{ cm}$ The area (A) of an equilateral triangle, $ A = \frac{\sqrt{3}}{4} \times a^2 $ On substituting $a = 12\sqrt{3}$ cm, $ A = \frac{\sqrt{3}}{4} \times (12\sqrt{3})^2 = \frac{\sqrt{3}}{4} \times 432 = 108\sqrt{3}\operatorname{ cm^2}$ Hence, the correct answer is $108\sqrt{3}\operatorname{ cm^2}$.
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Question : The height of an equilateral triangle is $9 \sqrt{3} \mathrm{~cm}$. What is the area of this equilateral triangle?
Option 1: $92 \sqrt{3} \mathrm{~cm}^2$
Option 2: $67 \sqrt{3} \mathrm{~cm}^2$
Option 3: $49 \sqrt{3} \mathrm{~cm}^2$
Option 4: $81 \sqrt{3} \mathrm{~cm}^2$
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
Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?
Option 1: $2\sqrt{3}$ cm
Option 2: $5\sqrt{3}$ cm
Option 3: $4\sqrt{3}$ cm
Option 4: $3\sqrt{3}$ cm
Question : The side of an equilateral triangle is 36 cm. What is the radius of the circle circumscribing this equilateral triangle?
Option 1: $13 \sqrt{3} \mathrm{~cm}$
Option 2: $10 \sqrt{3} \mathrm{~cm}$
Option 3: $12 \sqrt{3} \mathrm{~cm}$
Option 4: $9 \sqrt{3} \mathrm{~cm}$
Question : The perimeter of an equilateral triangle is 48 cm. Find its area (in cm2).
Option 1: $81\sqrt{3}$
Option 2: $8\sqrt{3}$
Option 3: $25\sqrt{3}$
Option 4: $64\sqrt{3}$
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