Question

Three identical coins , each of diameter 6 cm are placed as shown . Find the area of the shaded region between the coins .

Answer 1

Answer:

1 .458 cm²

Step-by-step explanation:

There will be Triangle formed between center of 3 coins

with each side = Radius + radius = Diameter = 6cm

Area of Triangle = (√3 / 4) *6²  = 9√3  = 9*1.732 = 15.588 cm²

Equilateral Triangle has 60° Angles

so each arc sector is at 60°

Area of Each sector = (60/360)πR²

Radius = Diameter/2

R =  6/2 = 3 cm  π = 3.14

= (1/6)(3.14)*3²

= 4.71

Area of Three Sectors = 3 * 4.71 = 14.13 cm²

Area of Shaded Region = 15.588 - 14.13  =  1 .458 cm²