Question
The diagram shows a sector AOB which is part of a circle with centre O and radius 6
cm and with angle AOB = 0.8 radians. The point C on OB is such that AC is
perpendicular to OB. The arc CD is part of a circle with centre O, where D lies on OA.
Find the area of the shaded region.
Solution
We are required to find the area of the shaded region.
It is evident from the diagram that;
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆ℎ𝑎𝑑𝑒𝑑 𝑅𝑒𝑔𝑖𝑜𝑛 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑇𝑟𝑎𝑖𝑔𝑛𝑙𝑒 𝐴𝑂𝐶 − 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟 𝐷𝑂𝐶
First, we find area of right-triangle AOB.
Expression for the area of a triangle for which two sides (a and b) and the included
angle (C ) is given;