Q7 of 27 Page 228

The area of an equilateral triangle is 49√3 cm2. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown in the figure. Find the area of the portion in the triangle not included in the circles.

Let the side of the triangle be ‘a’

As we know that,




⇒ a = 14 cm


Radius of each circle, r = a ÷ 2


⇒ r = 7 cm



Here, θ = 60°



⇒ AS = 25.67 sq.cm


Required area = Area(Δ ABC) – 3× areaof sector


⇒ Req. area = 49√3 – [3× 25.67]


⇒ 84.87 – 77.01


⇒ 7.86 sq.cm


∴ Area of the portion in the triangle not included in the circles is 7.86 sq.cm


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