Question

the area of an equilateral triangle ABC is 17320.5cm^. with each vertex of the triangle as centre,a circle is drawn with radius equal to half the length of the side of the triangle . find the area of the part that remains in triangle leaving the three sectors (use pie as 3.14nd root of 3 as 1.73205)

Answer 1

Given area = 17320.5
Let side =n
Using formula ........





I hope this is helpful.....

Answer 2

ABC is an equilateral triangle.
Therefore, ∠A = ∠B = ∠C = 60°
There are three sectors each making 60°.
Let x be the side of the equilateral triangle
Area of ΔABC = 17320.5 cm2
√3/4 × (x)2 = 17320.5
x = 200 cm
Therefore, Radius of the circles = 200/2 cm = 100 cm
Area of the sector = (60°/360°) × π r2 cm2
                                       = 1/6 × 3.14 × (100)2 cm2
                                       = 15700/3 cm2
 

Area of the shaded region = Area of equilateral triangle ABC – 3 × Area of sector
                                          = 17320.5 - 15700 cm2 = 1620.5 cm2

Hope this will help u....