Q35 of 37 Page 13

The area of an equilateral triangle is 100√3cm2. Taking each vertex as centre, a circle is described with a radius equal to half the length of the side of the triangle, as shown in the figure. Find the area of that part of the triangle which is not included in the circles [Take π=3.14 and √3=1.732]

Area of the shaded region


= Area of an equilateral triangle – Area of 3 sectors


Given: Area of equilateral ΔABC = 100√3cm2



⇒ a2 = 400


⇒ a = 20cm


It is given that radius is equal to half the length of the side


i.e.


Now,





= 157.14cm2


Hence, the area of the shaded region


= Area of ΔABC – Area of 3 sectors


= 100√3 – 157.14


= 100×1.732 – 157.14


=173.2 – 157.14


= 16.06 cm2


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