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Question 3
The shape of a garden is rectangular in the middle and semi-circular at the ends as shown in the diagram. Find the area and the perimeter of this garden [Length of rectangle is 20 - (3.5 + 3.5 meters)]


Solution

Given Total length = 20 m Diameter of semi circle = 7m
Radius of semi circle = 72=3.5m
Length of rectangular field = 20 - (3.5+3.5) = 20 - 7 = 13 m
Breadth of the rectangular field = 7m

Area of garden = Area of rectangular field + Area of the two semi-circular ends.

Area of rectangular field = l×b=13×7=91m2
Area of two semi circles = 2×12πr2=2×12×227×3.5×3.5=38.5m2
Area of garden = 91+38.5=129.5m2

Perimeter of garden =  2× length of the rectangular field +  2× length of the semi-circular arcs.

Now Perimeter of two semi cricles = 2×πr=2×227×3.5=22m
And Perimeter of garden = 22 + 13 + 13 = 48 m

Mathematics
NCERT Textbook
Standard VIII

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