Question

In the given figure [Fig.4], the area of an equilateral triangle ABC is 17320.5cm2 , with each vertex of the triangle taken as a centre, circle is drawn with radius equal to half the length of the side of the triangle. The area of the shaded region is:​

Answer 1

Answer-

Solution:

We use the formula for the area of the circle and the area of the triangle to solve the problem.

Given that, Area of equilateral ΔABC = 17320.5 cm2

√3/4 (side)2 = 17320.5 cm2

(side)2 = (17320.5 × 4)/√3 cm2

= (17320.5 × 4)/1.73205 cm2

side = √10000 × 4 cm²

= 100 × 2 cm

= 200 cm

Radius (r) = 1/2 × (length of side of triangle)

= 1/2 × 200 cm

= 100 cm

All interior angles of an equilateral traingle are of measure 60° and all 3 sectors are made using these interior angles.

∴ Angles subtended at the center by each sector (θ) = 60°

Area of each sector = θ/360° × πr2

Area of 3 sectors = 3 × 60°/360° × πr2

= 3 × 1/6 × 3.14 × (100 cm)2

= 15700 cm2

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

= 17320.5 cm2 - 15700 cm2

= 1620.5 cm2