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Example 3: A circle of 14 cm diameter is cut into two parts and joined along 14 cm
the shorter sides of a rectangle to form a figure as shown alongside. Find the
area and perimeter of this shape. 35 cm

Diameter 14
Solution: Radius of each of the two semicircles, r = = cm = 7 cm
2 2
Length of the rectangle, l = [35 – (7 + 7)] cm = (35 – 14) cm = 21 cm
Also from the diagram, breadth of the rectangle, b = Diameter of the circle = 14 cm.

So, the area of the whole figure = Area of the rectangle + area of the two semicircles

 1 
= lb×+ 2   2 r π 2  =× r 2
l b + π

22 2
7 cm
= 21 cm × 14 cm + ×() 2
7
22
2
×
= 294 cm + × 77 cm 2
7
2
2
2
= 294 cm + 154 cm = 448 cm .
Perimeter of the shape = l + πr + l + πr = 2l + 2πr
1
[Arc length of semi circle = × 2pr = pr]
2
22
×
= 221 cm + 2 × × 7 cm
7
= 42 cm + 44 cm = 86 cm.

Think and Answer

An ant moves around and brings food pieces by following tracks of different shapes as shown
in the figures. For which food piece would the ant have to take a longer round?
(a) (b) (c) 2.8 cm
1.5 cm
2.8 cm 2.8 cm
2 cm 2 cm

Example 4: In the given figure, the length of the side AD is 10 cm, side A
DC is 4 cm and side AB is 6 cm. Find the area of DACD. 10 cm
E 6 cm
Solution: For DACD, CD = base = 4 cm, AB = height = 6 cm

1
We have, area of DACD = × base × height D 4 cm C B
2
1
= × CD × AB Quick Check
2 Find the length of side EC in
1
= × 4 cm × 6 cm = 12 cm . the above figure.
2
2
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