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# Triangle ABC is an equilateral triangle

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Triangle ABC is an equilateral triangle and O is the center of its inscribed circle. If the area of the circle is  8sq cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form

Nov 6, 2020

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Triangle ABC is an equilateral triangle and O is the center of its inscribed circle. If the area of the circle is 8sq cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form

Hello Guest!

$$\frac{a}{2}=\frac{r}{tan(30°)}$$

$${\color{blue}r=\sqrt{\frac{A}{\pi}}}=\sqrt{\frac{8cm^2}{\pi}}=1.596\ cm$$

$$\frac{a}{2}=\frac{\sqrt{\frac{8cm^2}{\pi}}}{tan(30°)}=2.764\ cm^2$$

$$A_{ABC}=6\cdot ( \frac{1}{2}\cdot \frac{a}{2}\cdot r)=6\cdot ( \frac{1}{2}\cdot 2.765\ cm\cdot 1.596\ cm)$$

$$A_{ABC}=13.239\ cm^2$$

!

Nov 7, 2020