Question

there is a figure in which the diameter is 12cm and we have to find the area of the shaded region.figure is on this link--->http://www.twiddla.com/573294

Answer 1

Ok, so OD is radius and it is 12/2=6cm
the angle AOB=180-135=45 degree
So angle AOB=BAO=45 degree
Let's find the AB (AB=BO-equalsided triangle): \[\sin45^o=AB/AO \rightarrow AB=\sin45^o \times AO \rightarrow (AO=6, \sin45^o=\sqrt2/2) \rightarrow AB= 6 \times \sqrt2/2=3\sqrt2\]

Answer 2

So \[AB=3\sqrt2\]
Area of triangle ABO:\[AB^2/2=9 \times 2/2=9\]

Answer 3

the other triangle CDO is equal to ABO, so shaded area is \[9 \times 2=18 cm^2\]