Question

Find the area of the shaded region,where a circular arc of radius 6cm has been drawn with vertex O of an equilateral triangle OAB of side 12cm as centre

Answer 1

Answer:

• AB=OA+OB
• AB=6+6
• AB=12
• OAB=12
• AB=12/3
• AB =4
• OA=4
• OB=4

Answer 2

Answer:

$\sf{Area\:of\:shaded\:region=(36\sqrt3+\frac{660}{7})cm^{2}$

Step-by-step explanation:

$\sf{Area\:of\:shaded\:region=Area\:of\:triangle(60)+Area\:of\:major\:sector$

                                $\sf{=\frac{\sqrt3}{4}(a)^{2}+\frac{360-\theta}{360}\times\pi r^{2}$

                                $\sf{=\frac{\sqrt3}{4}(12)^{2}+\frac{360-60}{360}\times\frac{22}{7}\times(12)^{2}$

                                $\sf{=\frac{\sqrt3}{4}\times12\times12+\frac{360-60}{360}\times\frac{22}{7}\times12\times12$

                                $\sf{=\sqrt3\times3\times12+30\times\frac{22}{7}}$

                                $\sf{=(36\sqrt3+\frac{660}{7})cm^{2}$

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