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

ABCD is a rectangle with $A B = 14 cm$ and $B C = 7 cm$ . Taking DC,BC and AD as diameter, three semicircles are drawn. 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

60 c m^{2}

None of these

59 c m^{2}

59.5 c m^{2}

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given that, ABCD is a rectangle with AB = 14 cm , BC = 7cm and take DC, BC and AD as diameters.
We know that, the area of semicircle is

π r 2 2

.
Radius of the big semicircle is

142 = 7 cm

And radius of the two small semi circle is

72 cm

.
Calculating the area of big and small semi-circle.

2.12 π r 2 = 2 × 12 × 227 × 722

⇒ 38.5 C M 2

Now,

12 π r 2 = 12 × 227 × 72

⇒ 77 C M 2

Calculating the area of rectangle ABCD .

A r A B C D = L × B

⇒ 14 × 7

\Rightarrow

{cm}^{2}

Subtracting the area of bigger semi circle from the sum of the area of two semi circle and the area of rectangle,

98 + 38.5 − 77 = 59.5 c m 2

The area of the shaded region is 59.5

c m 2

.
Hence the correct option is 1.

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!