Question

❛ The area of an equilateral triangle is 1732.05cm². About each angular point as centre a circle is described with radius equal to half the length of the side of the triangle. Find the area of the triangle not included in the circles. ( Use π = 3.14 ) ❜

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Answer 1

Answer:

Given AB=BC=AC

Area of Equilateral △ ABC = 17320.5cm

2

∴

4

3

×AB

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 =

360

θ

×π×r

2

=3×

360

60

×3.14×100×100

=15700cm

2

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

=17320.5−15700

=1620.5cm

2

solution

I hope it will help you

Answer 2

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Given AB = BC = AC

Area of Equilateral A ABC=17320.5 cm2

:- √3/4 X AB = 17320.5

⟹AB = 200 cm

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 × r2

⟹ 3 x 60/360 x 3.14 X 100 X 100

⟹ 15700 cm

.:. Area of the shaded region =Area of equilateral triangle - Area of all sectors

⟹17320.5 – 15700

⟹1620.5 cm2