Question

OAB is a sector of the circle with centre O and radius 12cm . If m angle AOB = 60 o , find the difference between the areas of sectors AOB and triangle OAB ???

Answer 1

Area of Sector is Theta/360*pi*r^2 = 60/360*22/7*12*12 = 75.4 sq. cm.


Area of equilateral triangle.

Since the triangle is an equilateral triangle, then height is sqrt (12*12-6*6) = sqrt(144-36) = sqrt(108) = 10.39

Therefore area = 1/2 * 10.3923 * 12 = 10.39 * 6 = 62.35 sq. cm

Thus, the difference between areas of sector and triangle is = 75.4 - 62.35 = 13.05 sq. cm.