Q9 of 31 Page 183

Find the area of the shaded design in the figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter (use π = 3.14).

Given side of the square ABCD = 10 cm


Area of the square = side × side


⇒ Area of ABCD = 10 × 10 = 100 cm2


Also given that semicircles are drawn with each side of the square as diameter


Diameter = 10 cm


Radius = 5 cm


Let us mark the four unshaded areas as I, II, III and IV.


Area of I + Area III


= Area of square - Area of two semi-circles



= 21.5 cm2


Similarly, Area of II + Area of IV = 21.5 cm2


So, area of shaded region = ar of ABCD - ar (I + II + III + IV)


= (100 – 2 × 21.5) cm2


= 100 - 43


= 57 cm2


More from this chapter

All 31 →
7

In the given figure, ABMC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

 8

In the given figure, AB is a diameter, AC = 6 cm, BC = 8 cm. Find the shaded region.

 10

In the given figure, radius of the semicircle is 7 cm. Find the area of the circle drawn inside the semicircle.

 11

If the sum of circumferences of two circles of radii R1 and R2 is equal to the circumference of a circle of radius R, then which of the following choices is correct?