Question

Find the area of the shaded region in figure 4, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre and a sector of circle of radius 6 cm with centre B is made.


Figure- It has a circle (fully shaded) and with the sector there is a triangle which is shaded except for a sector at the corner with B as centre.

Is the answer (627/7 + 9 root 3) sq. cm. ??

Answer 1

 Area of sector outside triangle

=(angle O-angle AOB/360°)*$\pi$*$6^{2}$

=(300°/360°)*$\pi$*$6^{2}$

on solving we get

=94.28 sq cm

Area of triangle

=$\sqrt{3}/4$*$side^{2}$

on solving

=62.35 sq cm

Area of shaded region 

= 94.28 + 62.352 

= 156.632 sq cm

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Answer 2

in the attachment provided i have solved the answer

At least this is correct ?

Thank You......!!!!!!!!!
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Yours, Jahnavi.