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 60^{o}

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

Area of the segment =

=

= 102.62 CM^{2}

Area of the triangle = × OA^{2}

= × 14^{2}

= 84.870 CM^{2}

Area of the semi-circle =

Area of the segment - Area of the triangle

= 102.62 - 84.870

= 17.75 cm^{2}

Area of the semi-circle = × r^{2}

= × 7^{2}

= 76.96 cm^{2}

area enclosed by two arcs =

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

= 76.96 – 17.75

= 59.20 cm^{2} (approximately)

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Figure 13.29

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Figure 13.27

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