# An equilateral triangle is circumscribed inside a circle with a radius of 6. What is the area of the triangle?

Area of the equilateral triangle

Given triangle is equilateral and the radius of the circum circle is 6.

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The area of the equilateral triangle circumscribed inside a circle with a radius ( r ) can be calculated using the formula:

[ \text{Area} = \frac{\sqrt{3}}{4} \times (\text{side length})^2 ]

Given that the radius of the circle is 6, the side length of the equilateral triangle is twice the radius, so ( \text{side length} = 2 \times 6 = 12 ).

Substituting this into the formula:

[ \text{Area} = \frac{\sqrt{3}}{4} \times (12)^2 ]

[ \text{Area} = \frac{\sqrt{3}}{4} \times 144 ]

[ \text{Area} = 36\sqrt{3} ]

So, the area of the equilateral triangle is ( 36\sqrt{3} ) square units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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