In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm.

Question:

In the given figure, a circle is inscribed in an equilateral triangle ABC of side 12 cm. Find the radius of inscribed circle and the area of the shaded region. 

$[$ Use $\sqrt{3}=1.73, \pi=3.14]$

 

Solution:

We can find the radius of the incircle by using the formula

$r=\frac{2 \times \text { Area of triangle }}{\text { Perimeter of triangle }}=\frac{2 \times \frac{\sqrt{3}}{4} \times(12)^{2}}{3 \times 12}=2 \sqrt{3} \mathrm{~cm}$

Now, area of shaded region = Area of triangle − Area of circle

$=\frac{\sqrt{3}}{4} \times(12)^{2}-3.14 \times(2 \sqrt{3})^{2}$

$=62.28-37.68$

$=24.6 \mathrm{~cm}^{2}$

Hence, the area of shaded region is 24.6 cm2

 

 

 

 

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