Q44 of 45 Page 12

In the given figure, ABCD is a rectangle of dimensions 21 cm × 14 cm. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure.

(CBSE 2017)

Required shaded area = area of rectangle - area of semicircle as diameter BC


Now,


Area of rectangle = length × breadth = AB × BC


Diameter of semicircle, BC = 14 cm


⇒ Radius of semicircle,


And area of semicircle of radius 'r' = 


Therefore,


Required area 
   
= 294 - 11(7)
= 294 - 77
= 217 cm2


Now, let us calculate the Perimeter of the shaded region,

We know that perimeter of a semi-circle = πr, where r is the radius of the circle.

Therefore, perimeter of semi-circle = 22/7 × 7 = 22cm

And from the figure we can see that,

Perimeter of the figure = 2.Length of the rectangle + Breadth of the rectangle + Perimeter of the semi-circle
Perimeter of the figure = 2 × 21 + 14 + 7 = 42 + 21 = 63 cm


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41

A child makes a poster on a chart paper drawing a square ABCD of side 14cm. She draws four circles with centre A,B,C and D in which she suggests different ways to save energy. The circles are drawn in such away that each circle touches externally two of the three remaining circles (Fig.15.74). In the shaded region she writes a message ‘Save Energy’. Find the perimeter and area of the shaded region.

(CBSE 2015)

 42

In fig. 7, are shown two arcs PAQ and PBQ. Arc PAQ is a part of circle with center O and radius OP while arc PBQ is a semi-circle drawn on PQ as diameter with center M. If OP = PQ = 10 cm, show that area of shaded region is.

(CBSE 2016)

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An elastic belt is placed around the rim of a pulley of radius 5 cm. (Fig. 10) From one-point C on the belt, the elastic belt is pulled directly away from the center O of the pulley until it is at P, 10 cm from the point O. Find the length of belt that is still in contact with the pulley. Also find the shaded area.

(CBSE 2016)

 45

In the given figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where O and O′ are centers of the circles. Find the area of shaded region.

(CBSE 2017)