Area of Equilateral Triangle with Inradius R

Question

What is the area of an equilateral triangle whose inscribed circle has radius R?

Accepted Answer

D. For an equilateral triangle of side $a$, inradius $r = R = \frac{a}{2\sqrt{3}} \Rightarrow a = 2\sqrt{3}R$. Area = $\frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} (2\sqrt{3}R)^2 = \frac{\sqrt{3}}{4} (12R^2) = 3\sqrt{3}R^2$.

Answer

$4R^2$

Answer

$4\sqrt{3}R^2$

Answer

$(3 + 2\sqrt{2})R^2$

Answer

$3\sqrt{3}R^2$

Area of Equilateral Triangle with Inradius R

Explanation

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