The area of an equilateral triangle ABC is 17320.5cm? 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 t = 3.14 and 13 = 1.73205)
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Given AB=BC=AC
Area of Equilateral △ ABC = 17320.5cm / 2
∴ 4 × AB
3 × 2
=17320.5
∴ AB =200cm
Also, AB=2AD
∴ AD=100 cm =radius
Area of sector DAE + Area of sector DBF + Area of sector FCE.
We know that area of sector = 0
360 ×π×r
=3× 360 ×3.14×100×100
60
=15700cm²
∴ Area of the shaded region = Area of equilateral triangle − Area of all sectors
=17320.5−15700
=1620.5cm²
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