Question

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 Figure). Find the area of the shaded region. (Use π = 314 and √3 = 1.73205).

Answer 1

(i) Area of an equilateral ∆ABC : 

= 17320.5 cm²

(ii) Area formed by centre A: 

r = 100 cm, θ = 60°

Similarly 

Area of sectors formed by centres B and C is 5233 sq.cm. 

∴ Total Area of THREE sectors : = 3 × 5233 = 15699 sq.cm. 

∴ Area of shaded region : 

= Area of an equilateral Triangle – Area of three sectors. 

= 17320.5 – 15699 

= 1621.5 sq. cm.