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Question 10
The area of an equilateral triangle ABC is 17320.5cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Fig. 12.28). Find the area of the shaded region. (Use π=3.14and3=1.73205)


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Solution

ABC is an equilateral triangle.
A=B=C=60
There are three sectors each making 60.
Area of ΔABC=17320.5 cm2
34×(side)2=17320.5(side)2=17320.5×41.73205(side)2=4×104side=200cm
Radius of the circles =2002cm=100cm
Area of the sector =(60360)×πr2cm2
=16×3.14×(100)2cm2
=157003cm2
Area of 3 sectors =3×157003=15700cm2
Area of the shaded region = Area of equilateral triangle ABC - Area of 3 sectors
=17320.515700cm2=1620.5cm2


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