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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)

NCERT cbse solutions areas related to circles

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


 


Posted in : Algebra, Areas related to Circles, Circles


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