Page 250 - Start Up Mathematics_7

11. Two circles are drawn inside a big circle of diameter 24 cm. The
1 2
diameter of the two circles are and of the diameter of the big
3 3
circle as shown in the adjoining figure. Find the ratio of the areas
of the shaded part to the unshaded part of the circle.

12. Inside a rectangular garden 24 m long and 18 m wide, a 2 m margin
is left for planting tulip flowers. If 4 tulip stems can be planted in
2
1 m and each tulip stem costs ` 30, find the total expenditure
incurred.

Area of Some More Plane Figures a

Sum of parallel sides
Area of Trapezium = × height h
2
a + b
= × h
2 b
1
Area of Rhombus = (Product of diagonals) d
2 1

1
= × d × d d
2 1 2 2
Example 32: A path 3 m wide runs outside and around a
rectangular park of length 120 m and breadth 65 m.
Find the area of the path in hectare. 3 m
Solution: Length of the rectangular park = 120 m 65 m
Breadth of the rectangular park = 65 m 120 m
Width of the path = 3 m

Length of the park alongwith path = 120 + 3 + 3 = 126 m
Breadth of the park alongwith path = 65 + 3 + 3 = 71 m
Area of the park = l × b = 120 × 65 = 7,800 m 2
Area of the park alongwith path = 126 × 71 = 8,946 m 2

Area of the path = 8,946 – 7,800 = 1,146 m 2
1,146
Area of the park in hectares = = 0.1146 hectares
10,000
Example 33: A picture is painted on a cardboard 8 cm long 1.5 cm
and 5 cm wide such that there is a margin of
1.5 cm along each of its sides. Find the total 5 cm
area of the margin. (NCERT)
Solution: Length of the cardboard = 8 cm
Width of the cardboard = 5 cm 8 cm
Margin along each side = 1.5 cm

Length of the painted portion = length of cardboard – margin along both sides
= 8 – (1.5 + 1.5) = 8 – 3 = 5 cm
Width of the painted portion = Width of cardboard – margin along both sides

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