Book Online Demo

Check Your IQ

Try Test

Courses

Offline Centres

In the following figure, ABCD is a trapezium with AB || DC, $A B = 18$ cm, $D C = 32$ cm and distance between AB and DC is 14cm. If arcs of equal radii $7$ cm with centres A, B, C and D have been drawn, then the area of the shaded region of the figure from the following choices is:

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

121 cm 2

135 cm 2

154 cm 2

196 cm 2

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

It is given that,

A B = 18

cm,

D C = 32

cm and distance between AB and DC is 14 cm.
Question Image

Obtain the area of a trapezium.
The area of the trapezium is given by,

A = \frac{1}{2} \times Sum of parallel sides \times Distanca between parallel sides

Here, the distance between the parallel sides is 14 cm.
Substituting the values in the formula, we get,

A = \frac{1}{2} (AB + CD) 14

A = \frac{1}{2} (18 + 32) 14

A = 350 {cm}^{2}

Obtain the area of the circle, we get,

A ′ = π r 2 A ′ = π (7) 2 A ′ = 154 cm 2

Thus, from figure the area of the shaded region is,

A s = A − A ′ A s = 350 − 154 A s = 196 cm 2

The area of the shaded region is

196 cm 2

.
Hence, option 4) is correct.

Watch 3-min video & get full concept clarity