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Area of a Sector

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This item is taken from IGCSE Mathematics (0580) Paper 2 (Extended) examination on October/November 2007. 

To answer this item, let us recall first the necessary formula needed for solving this item. This item involves AREA OF SECTORS.
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Looking at the figure, there are two semicircles involved. 
IGCSE,mathematics,areas,circles,semicircles
Let us find the area of each semicircle. 
The bigger semicircle has a diameter of 24 cm. It means that its radius is equal to 12 cm. The area of the bigger semicircle is
IGCSE,mathematics,areas,circles,semicircles
On the other hand, the smaller semicircle has a diameter of 12 cm. It means that it has a radius of 6 cm. Its area is 
IGCSE,mathematics,areas,circles,semicircles
Since we are only finding the area of the shaded region, 
IGCSE,mathematics,areas,circles,semicircles

IGCSE,mathematics,areas,circles,semicircles

Therefore, the area of the shaded region is approximately 170 centimetres.

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