Q. 45.0( 3 Votes )

There are two arcs of (O, OA) and of (M, MA) as shown in figure 13.24. Find the area enclosed by two arcs.



Figure 13.24

Answer :

from the figure we can notice all these


1. OAB is an equilateral triangle


( All the sides are equal)


2. OAPB is a minor segment with Radius 14 cm, the angle (θ) between them is 60o


3. ABQ is a semi-circle with centre as M radius 7 cm


Area of the segment =


=


= 102.62 CM2


Area of the triangle = × OA2


= × 142


= 84.870 CM2


Area of the semi-circle =


Area of the segment - Area of the triangle


= 102.62 - 84.870


= 17.75 cm2


Area of the semi-circle = × r2


= × 72


= 76.96 cm2


area enclosed by two arcs =


Area of the semi-circle - Area of the semi-circle


= 76.96 – 17.75


= 59.20 cm2 (approximately)


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