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The area of an equilateral triangle ABC is 17320.5 cm2. 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 the given figure). Find the area of shaded region. [Use π = 3.14 and √ 3 = 1.73205]

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Let the side of the equilateral triangle be a.

Area of equilateral triangle = 17320.5 cm2

Each sector is of measure 60°.

Area of sector ADEF = 60o/360o x π r2

= 1/6 x π x 1002 = (3.14 x 10000)/6

=15700/3 cm2  

Area of shaded region = Area of equilateral triangle − 3 × Area of each sector

=17320.5 - 3 x 15700/3

= 17320.5 - 15700 = 1620.5 cm2

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