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in Perimeter and Area of Plane Figures by (23.5k points)
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A cow is tethered at corner A by a rope. Neither the cow nor the rope is allowed to enter DABC. ∠A = 30º, AB = AC = 10 m and BC = 6 cm. What is the area that can be grazed by the cow if the length of the rope is 8 m.

(a) \(133\frac{1}{6}\) π sq. m 

(b) 121π sq. m 

(c) 132π sq. m 

(d) \(\frac{176}{3}\) π sq. m

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(d) \(\frac{176}{3}\pi\) sq. cm

Given : AB = AC = 10 m, BC = 6 m and ∠A = 30º. The area that the cow can graze is the area of the circle with centre A and radius 8 m. But the cow is not allowed to enter the sector ADE formed inside DABC with ∠A = 30° and AD = AE = 8 cm. 

∴ Area grazed = Area of circle – Area of sector ADE

= πr2 - πr2\(\frac{30°}{360°}\) = πr2 \(\bigg(1-\frac{30°}{360°}\bigg)\)

= π x 64 x \(\frac{11}{12}\) = \(\frac{176}{3}\pi\) sq. cm

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