Question

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)​

Answer 1

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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Answer 2

Answer:

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