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Areas Related to Circles

There is a design on a square window glass as shown below.

The shaded portion is coloured yellow. They are the segments of a circle whose radius is 7 cm and the angle of the sector is 90°. Rest all the portion is transparent. Can we calculate the area of the shaded portion?

To calculate the area of the shaded portion, we should know how to calculate the area of segments of the circle.

Firstly, let us know the formula to find the area of the segment of a circle.

The above figure shows a circle with radius r. OPXQ is a sector of the circle. The angle of sector is θ. PXQP is a segment of the circle.

From the figure, we can see that

Area of the segment PXQP = area of the sector OPXQ − area of the triangle OPQ

− area of ΔOPQ

Using this formula, we can calculate the area of the shaded portion in the figure discussed in the beginning.

In that figure, the radius of the circle is given as 7 cm and angle of the sector 90°. To calculate the area of the shaded portion, we will calculate the area of each segment. Let us draw the circle whose segment has been shown in the given figure. On drawing the circle, we obtain the following figure.

The sector has the angle 90° at the centre, i.e. AOB = 90°.

Let us draw…

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