Q5 of 36 Page 253

The length of a side of a square garden ABCD is 70 m. A minor segment of (O, OA) is drawn on each of two opposite sides for developing lawn, as shown in figure 13.25. Find the area of the lawn.


figure 13.25


side of a square garden ABCD (a) = 70 m


From the fig. in the below we can see that


1. OAXD is a segment


2. OAD is an right-angled triangle.


3. AXD is a minor segment


OA, OD are the radii of the segment


from the triangle OAD


AD2 = OA2 + OD2


702 = r2 + r2


2r2 = 4900


r2 = 2450


r = √2450


Area of minor segment = Area of segment - Area of triangle



= - × OA2


= - ×


= 1924.22 – 1225


=699.22 cm2


= 700 cm2


since AXD, BYC are same


∴ Area of lawn = 2 × area of minor segment


= 2 × 700


= 1400 cm2


More from this chapter

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3

If a chord of (O, 20) subtends right angle at O, find the area of the minor segment.

 4

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


 6

ABCD is a square of side 20 cm. Find the area of blue coloured region formed by the semi-circles drawn on each side as shown in figure 13.26. ( = 3.14)


figure 13.26.


 7

On a circular table top of radius 30 cm a design is formed leaving an equilateral triangle inscribed in a circle. Find the area of the design. (π = 3.14)