Find the area of the shaded region in the given figure,

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Question:

Find the area of the shaded region in the given figure, where a circular arc of radius 6 cm has been drawn with vertex of an equilateral triangle of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.  $[$ Use $\sqrt{3}=1.73, \pi=3.14]$

Solution:

In equilateral traingle all the angles are of  60°
∴ ∠ABO = ∠AOB = 60°
 Area of the shaded region = (Area of triangle  AOB − Area of sector having central angle 60°) + Area of sector having central angle (360° − 60°)

$=\frac{\sqrt{3}}{4}(\mathrm{AB})^{2}-\frac{60^{\circ}}{360^{\circ}} \pi(6)^{2}+\frac{300^{\circ}}{360^{\circ}} \pi(6)^{2}$

$=\frac{1.73}{4}(12)^{2}-\frac{1}{6} \times 3.14(6)^{2}+\frac{5}{6} \times 3.14(6)^{2}$

$=62.28-18.84+94.2$

$=137.64 \mathrm{~cm}^{2}$

Hence, the area of shaded region is 137.64 cm2

 

 

 

 

 

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