Question

the area of an equilateral∆ABC is 17320.5with eaach vertex of the triangle as centre,a circle is drawn with radius equal to half the length of the side of the triangle​

Answer 1

Step-by-step explanation:

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