the area of an equilateral triangle is 173 20.5 cm square about each angular point as a circle is described with radius equal to half the length of the sides of the triangle find the area of the triangle not included in the circle
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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
Step-by-step explanation:
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