Question #2eaa7

1 Answer
CW
Sep 22, 2016

see explanation.

Explanation:

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As can be seen, OAB is an equilateral triangle with sides =10, =>⇒ angle AOB = 60^@60∘

a) perimeter of shaded region = arc CD+arc CE +arc CD (arc CE = arc DE) :

=> 2pi(15)xx60/360 + 2xx(2pi(5)xx120/360)⇒2π(15)×60360+2×(2π(5)×120360)

=5pi+(20pi)/3 = (35pi)/3=5π+20π3=35π3 (proved)

b) Area of the shaded region (A_s)(As)= Area OCD - Area OAB - 2(Area ACE). (note Area ACE = Area BDE)

=> A_s = pi(15)^2xx60/360-sqrt3/4(10)^2-2(pi(5)^2xx120/360)⇒As=π(15)2×60360−√34(10)2−2(π(5)2×120360)

=22.15=22.15

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