Question

the area of an equilateral triangle is 49√3cm^2.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 position in the triangle not included in the circle

Answer 1

The correct diagram is this.
By Pythagoras theorem, height of the equilateral triangle is
$\sqrt{3} a \div 2$
Thus,
$(1 \div 2) \times a \times ( \sqrt{3} a \div 2) = 49 \sqrt{3}$
'a' comes out to be 196cm.
Thus, radii of circles will be 98cm.
Every circle forms a sector of 60° inside the triangle, which is one-sixth of the area of the circle, as
$60 \div 360 = 1 \div 6$
and there are 3 such sectors in the triangle, so, we can say there is an area equivalent to a semicircle in the triangle occupied by the circle.
Subtract the semicircle's area from the triangle and you'll have the answer.
Hope it helps.