Q36 of 37 Page 13

In an equilateral triangle of side 12cm, a circle is inscribed touching its sides. Find the area of the portion of the triangle not included in the circle. [Take √3=1.73 and π=3.14]


Area of shaded region = Area of ΔABC – Area of circle


Given side of triangle = 12cm




= 36√3cm2


Now, we have to find the area of a circle. For that we need a radius.


Draw AD ⊥ BC


So, In BDO




⇒ r = 2√3cm


Now, Area of circle = πr2


= 3.14 × (2√3)2


= 37.68cm2


Area of shaded region = Area of ΔABC – Area of circle


= 36√3 – 37.68


= 36(1.73) – 37.68


= 24.6cm2


Hence, the area of the portion of the triangle not included in the circle is 24.6cm2


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