Question

In the given figure, ABCD is a rectangle inscribed in a circle having length 8 cm and breadth 6 cm. If π = 3.14, then the area of the shaded region is:

पर्याय

• 264 cm²

• 266 cm²

• 272 cm²

• 254 cm²

• None of the above. 

Answer 1

None of the above

Explanation: 

All options are incorrect; the correct answer is 30.5 cm.

Join AC.
Now, AC is the diameter of the circle.

We have:

AC2 = AB2 + BC2 [By pythagoras' theorem]

⇒ AC² = {(8)² + (6)²} cm² 

⇒ AC² = (64 + 36) cm²   

⇒ AC² = 100 cm² 

∴ Radius of the circle`=10/2 "cm"`

= 5 cm

Now,

Area of the shaded region = Area of the circle with radius 5 cm − Area of the rectangle ABCD    

`=|(3.14xx5xx5)-(8xx6)| "cm"^2`

`=|(314/100xx25)-48|  "cm"^2`

`=(157/2-48) "cm" ^2`  

`=61/2 "cm" ^2`

= 30.5 cm²