Question

The area of an equilateral triangle ABC is 17320.5 cm?. 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. Find the area of the shaded region.
(Use π = 3.14 and √3 = 1.73205)​

Answer 1

$answer$

Given AB=BC=AC

Area of Equilateral △ ABC = 17320.5cm2

∴ 43×AB2 =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 =360θ×π×r2

=3×36060×3.14×100×100

=15700cm2

∴ Area of the shaded region = Area of equilateral triangle − Area of all sectors

=17320.5−15700

=1620.5cm2