The area of an equilateral triangle is $493 cm 2$ . Taking each vertex as centre, circles are described with radius equal to half the length of the side of the triangle. Find the area of the part of the riangle not included in the circles. $(T a k e 3 = 1.73, π = 227)$

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7.77 c m^{2}

8 c m^{2}

7.23 c m^{2}

9 c m^{2}

answer is A.

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Detailed Solution

Given that, the area of an equilateral triangle is

493 c m 2

and here we take each vertex as centre, and circles are described with radius equal to half of the side of the triangle.
We know that, the area of equilateral triangle is

34 × side 2

and the formula used to find the area of circle is

π r 2

.
Calculating the area of equilateral triangle to find the side.

34 × side 2 = 493

\Rightarrow

(Side) 2 = 72 × 22

\Rightarrow

side

= 14 cm

The radius of the circle is half of the side of the triangle 7 cm.
Calculating the area of the triangle not included in the circle by subtracting the area of three sectors having central angle 60° from the area of triangle.