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Question
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 `sqrt3 `= 1.73205]
Solution
Let the side of the equilateral triangle be a.
Area of equilateral triangle = 17320.5 cm2
sqrt3/4(s)^2 = 17320.5
1.7320/4a^2 = 17320.5
a2 = 4 x 10000
a = 200 cm
Each sector is of measure 60°.
Area of sector ADEF = `60^@/360^@ xx pixxr^2`
`=1/6xxpixx(100)^2`
`=(3.14xx10000)/6`
`= 15700/3 cm^2`
Area of shaded region = Area of equilateral triangle − 3 × Area of each sector
`= 17320.5 - 3xx 15700/3`
= 17320.5-15700 = 1620.5 cm2
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