Question

In the figure ABCD is a square of side 10cm.

semi-circles are drawn with each side of

square as diameter. Find the area of

i) the unshaded region

ii) the shaded region​

Answer 1

Answer:

Given

Side of square ABCD = 10 cm

Area of square ABCD = (side)²

= (10)²

= 100 cm²

Given semicircle is drawn with side of square as diameter,

So, Diameter of semicircle = Side of square = 10 cm

Radius of semicircle= side = 20 = 5 cm

Area of semi circle AD = x area of circle

X mr²

X1 -X πT X (5)²

= 3.14 X 25

2

Since radius is same for semi-circle AD, BC, AB, CD

Area of semi circle AD = Area of semi circle BC = Area of semi circle AB

= Area of semi circle CD:

Let us mark the unshaded

region as I, II, III, and IV.

Area of shaded region

3.14 x 25

2

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IV

= Area of ABCD - (Area of I + II + III+IV)

Area of region I + Area of region III

= Area of square ABCD

- (Area of semicircle AD + area of semi circle BC)

Area of region II + Area of region IV

= Area of square ABCD

- (Area of semicircle AB+ area of semi circle CD)

So, Area of region (I+II+III+IV)

= 2(Area of square ABCD) - (Area of semicircle AD + BC + AB + CD)

Putting values

2(100)-(

3.14 x 25 3.14 X 25

+ 2

= 200-4x 3.14 x 25

2

= 200-2 × 3.14 x 25

= 200 - 157

= 43 cm²

Now,

Area of shaded region

= Area of ABCD - (Area of I + II + III + IV)

= 100 - 43

= 57 cm²

Hence, area of shaded region = 57 cm²