Question

In the following figure, ABCD is a rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180° have been cut off. Calculate:
(i)the area of the shaded region.
(ii)the length of the boundary of the shaded region.​

Answer 1

Answer:

The Area of shaded region is 126 cm² and Length of the boundary of the shaded region is  84 cm.  

Step-by-step explanation:

GIVEN :

Length of a rectangle AB = 20 cm

Breadth of a rectangle ,BC = 14 cm

Diameter of circle = Breadth of a rectangle = 14 cm

Radius of Semicircle = diameter/2 =  14/2 = 7 cm

Area Of Rectangle = length X breadth

= 20 × 14

= 280 cm²

AREA OF RECTANGLE = 280 cm²  

Area Of 2  Semicircle = 2 × ½ πr²

= (π) × 7²

= 49π cm²

Area Of 2  Semicircle = 49π cm²

(i) Area of shaded region = Area of rectangle -  Area of 2 semicircles

Area Of Shaded Region = (280 - 49 π)  

= (280 -  49 × 22/7)

= (280 - 7 × 22)

= 280 -  154

= 126 cm²

Area of shaded region = 126 cm²

(ii) Length of the boundary of the shaded region = AB + DC + 2 × circumference of semicircle

= AB + DC + 2 × πr

= 20 + 20 + 2 × 22/7 × 7

= 40 + 44

= 84 cm

Length of the boundary of the shaded region = 84 cm

Hence, the Area of shaded region is 126 cm² and Length of the boundary of the shaded region is  84 cm.  

HOPE THIS ANSWER WILL HELP YOU….

Here are more questions of the same chapter :

In the following figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

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From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in the following figure. Find the area of the remaining (Shaded) portion of the square. (Use $(\pi=\frac{22}{7})$)

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Answer 2

Answer:

Step-by-step explanation:

Given that,

AB=20CMand BC=14cm,

Area of shaded region =?

The length of the boundary of the shaded region =?

So,A.T.Q,

Area of rectangle =l×b,

=20×14=280cm square,

Now, area of 2 sector with radius 7and angle 180,

= 180/360×22/7×7×7×2=154cm square

Now area of rectangle - area of 2 sectors,

=280cm square-154 cm square

=126cm square...(that's area of shaded region)

Now,

Length of boundary = 2×20+2×22/7=84cm

HOPE THIS HELPS YOU,.....