AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In the figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

85 cm 2

83 cm 2

80 cm 2

84 cm 2

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that, side of Square ABCD = 14cm.
Therefore,

Area of Square A B C D = (Side) 2 = (14) 2 = 196 cm 2

Diameter of semi-circle = side of Square =14 cm.
Now, find radius of semi-circle.
Radius of semi-circle =

= side 2 = 142 = 7 cm

Area of Semi- Circle

= 12 ×

area of circle

= 12 × π r 2 = 12 × 227 × (7) 2 = 11 × 7 = 77 cm 2

Let us mark the Shaded region as I, II, III, and IV.
Question Image

Area of region = (I + I I + I I I + I V) = 2 (Area of Square A B C D) − (Area of Semi-circle A D + B C + A B + C D) = 2 (196) − (77 + 77 + 77 + 77) = 200 − 4 × 77 = 392 − 308 = 84 cm 2

The area of the shaded region is

84 cm 2

.
The correct option is (4).

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!