# Areas related to Circles Ncert solutions Chapter 12 Exercise 12.3 Question 10

Areas related to Circles ncert solutions Chapter 12 Exercise 12.3 Question 10

10.    The area of an equilateral triangle ABC is 17320.5 $cm^2$. With each vertex of the triangle as center, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the shaded region (blue). (Use $\pi=3.14$ and $\sqrt{3}=1.73205$)

Solution:

Area of region shaded in blue= Area of equilateral $\triangle ABC$-Area of region shaded in orange         (1)

Area of equilateral $\triangle ABC$=17320.5 $cm^2$       {Given}           (2)

$\Rightarrow \frac{\sqrt{3}}{4} \times side^2=17320.5$

$\Rightarrow \frac{1.73205}{4} \times side^2=17320.5$

$\Rightarrow side^2=\frac{17320.5 \times 4}{1.73205}$
$\Rightarrow side= 200$ cm

$\Rightarrow$ Radius of circle=r=200/2=100 cm

Area shaded in orange = Area of three sectors of circle

$=3 \times \pi.r^2 \times \frac{\theta}{360}=3 \times 3.14 \times 100 \times 100 \times \frac{60}{360}$

$=15700$ $cm^2$                (3)

Putting (2) and (3) in (1), we get

Area of region shaded in blue=17320.5-15700=1620.5 $cm^2$

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