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In the diagram below, $CAD$ is a sector with centre $A$ and $EBD$ is a semicircle with diameter $ED$. Given that $AB=18cm$ and angle $CAD=\pi/3$ radian. Find

(a) The perimeter of the shaded region.

(b) The area of the shaded region.

enter image description here

I'm assuming that $AB=CD$ and have worked out that $CD=37.704cm$ Please help as it is midnight in my region and I would need to hand in my homework tomorrow.

Robert Z
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bryan
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1 Answers1

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Hint. Let $O=(E+D)/2$ be the center of the semi-circle then $BO$ is orthogonal to $AB$.Then $\angle CAD=\pi/3$ implies that $\triangle ABO$ is a right triangle with angles $30^{\circ}-60^{\circ}-90^{\circ}$. Moreover, $\triangle ACD$ is equilateral.

Can you take it from here?

Robert Z
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