Question

In an equilateral triangle of side $12$ cm , a circle is inscribed touching its sides . Find the area of the portion of the triangle not included in the circle . Take $\sqrt{3}=1.73$ and $\pi =3.14$ .

Answer 1

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side of equilateral triangle is 12 cm

height = $\frac{\sqrt{3}}{2}a$ $=\frac{\sqrt{3}}{2}\times 12$ $=6\sqrt{3}cm$

$tan{30}^{\circ }=\frac{r}{6}$

$\frac{1}{\sqrt{3}}=\frac{r}{6}$

$\frac{6}{\sqrt{3}}=r$

$\therefore r=\frac{6}{\sqrt{3}}cm$

area not included = $\frac{\sqrt{3}}{4}{a}^2-\pi r^2$

$=\frac{\sqrt{3}}{4}\times (12{)}^2-\pi \times (\frac{6}{\sqrt{3}}{)}^2$

$=\frac{\sqrt{3}}{4}\times 144-\pi \times \frac{36}{3}$

$=36\sqrt{3}-3.14\times 12$

$=62.35-37.68$

$=24.67c{m}^2$