Question

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]

Answer 1

Area of the shaded region

= Area of an equilateral triangle – Area of 3 sectors

Given: Area of equilateral ΔABC = 100√3cm²

√3/4 a² = 100√3

⇒ a² = 400

⇒ a = 20cm

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

i.e.  r = a/2 = 20/2 = 10 cm

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