CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

Find the area of shaded region, if in parallelogram ABCD, PBQ=SDR = 60o, BP=BQ=SD=RD= 21 cm, BC = 45 cm and MN = 20 cm.

A
231 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
438 cm2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
669 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
897 cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 438 cm2
As BP=BQ= radius, PQ is part of circle, region sector is sector with PBQ is 60o
Similarly
As SD=RD= radius, SR is part of circle, region SDR is sector with SDR is 60o

Area of shaded region
= area of parallelogram ABCD
- area of sector PBQ
- area of sector SDR

Area of parallelogram = base×height
= BC×MN = 45×20 = 900 cm2

Area of sector PBQ = angle360o×πr2
= 60o360o×227×212 = 16×227×441 = 11×21
= 231 cm2

As sector PBQ and SDR has same angle and radius, these two sector will have same area.
Area of sector SDR = Area of sector PBQ = 231 cm2

Area of shaded region = 900 - 231 - 231 = 438 cm2

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image