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Question

On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design.

[Use 3=1.73andπ=227.]


Solution

Join AO and extend it to D on BC.

Radius of the circle, r = 42 cm

OCD=30ocos 30o=DCOC32=DC42DC=213BC=2×DC=2×213=72.66cmsin 30o=ODOC12=OD42OD=21 cm

Now, AD=AO+OD=42+21=63 cm

Area of the shaded region = Area of circle – Area of triangle ABC

=π(OA)212×AD×AB=227×(42)212×63×72.66=55442288.79=3255.21 cm2
 

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