find the area of the shaded region
Asked by debasish2345 | 26th Nov, 2009, 08:32: AM
Let C and D be the centre of the circle where AD = 12cm and BC = 4 cm
In triangle CDE,
CD2 = DE2 + CE2
CE2 = CD2 - DE2
CE2 = 162 - 82 = 192
So, CE = 83
i.e Height of the trapezium, h = 83
Area of the trapezium = 1/2 x (BC + AD) x h
= 1/2 x 16 x 83
= 643 cm2
In triangle CDE,
tan x = 83 / 8
x = 60o
So, FCE = 30o
i.e BCF = 90o + 30o = 120o
Now, Area of sector ADF = x (12)2 x (60/360) = 75.36 cm2
Now, Area of sector BFC = x (4)2 x (120/360) = 16.74 cm2
Area of shaded region =Area of Trapezium ABCD - (Area of Sector ADF + Area of Sector BFC)
= 643 - (75.36 + 16.74) = 18.75 cm2
Answered by | 11th Dec, 2009, 02:51: PM
Kindly Sign up for a personalised experience
- Ask Study Doubts
- Sample Papers
- Past Year Papers
- Textbook Solutions
Sign Up
Verify mobile number
Enter the OTP sent to your number
Change