The area of an equilateral triangle ABC is 17320.5 cm². 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 (See the given figure). Find the area of shaded region. [Use π = 3.14 and]

plz answer this question....and plz tell me step by step......can anyone...help me..

area of ABC = 1.743205/4 a²

17320.5 = 1.73205/4 a²

a² = 17320.5 * 4 / 1.73205

a² = 10000 * 4

 a² = 40000

a = 200cm

radius = a/2

 radius = 100 cm

area of three sectors = 3( theta/360 pie r²)

= 3(60/360 * 3.14 * 100  *100)

= 3(1/6 * 314 * 100)

=134*50

= 15700cm²

area of shaded region = aria of ABC - areaof three sectors

area of shaded region = 17320.5 - 15700

area of shaded region = 1620.5 cm²

 guys thankyou.....

 what matttttttt  said is correct.

1620.5 cm²is the area of the shaded region! :D

say: ABC is an equilateral triangle.

as all angles equals  60°

Area of ΔABC = 17320.5 

side= a

as we know √3/4.(side)²  = 17320.5

(a)²  = 17320.5 × 4/1.73205

(a)²  = 4 × 104 

a  = 200 cm

Radius of the circles = 200/2 cm = 100 cm

Area of 1 sector = (60°/360°) × π r² 

= 1/6 × 3.14 × (100)²

= 15700/3 

Area of 3 sectors = 3 × 15700/3 = 15700

Area of the shaded region = Area of equilateral ΔABC - Area of 3 sectors

= 17320.5 - 15700

= 1620.5