In the given fig. circle are drawn by taking vertices A,B and C of an equilateral triangle of side 20cm to intersect the sides BC, CA and AB at their points D,E and F. Find the area of shaded region.
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taking E,D and F as mid points of sides AC,BC and BA.
therefore,AE=EC=DC=BD=BF=AF=10cm.
now,as triangle is equilateral,so its all angles are 60.
therefore,thita for all forming sectors would also be 60 with radius of 10cm.
area of saded region = area of traingle-area of 3 sectors
= √3×20×20÷4 - 3×(60/360×22/7×10×10)
= 100√3 - 1100/7
after putting value of √3=1.73,
=100×1.73 - 1100/7
= 173 - 1100/7
answer= 111/7
or,
15.85cm²
therefore,AE=EC=DC=BD=BF=AF=10cm.
now,as triangle is equilateral,so its all angles are 60.
therefore,thita for all forming sectors would also be 60 with radius of 10cm.
area of saded region = area of traingle-area of 3 sectors
= √3×20×20÷4 - 3×(60/360×22/7×10×10)
= 100√3 - 1100/7
after putting value of √3=1.73,
=100×1.73 - 1100/7
= 173 - 1100/7
answer= 111/7
or,
15.85cm²
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