Area of a Sector

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.

Looking at the figure, there are two semicircles involved. 

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

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 

Since we are only finding the area of the shaded region, 

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

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