Page 204 - Start Up Mathematics_6

Example 20: The cost of cultivating a rectangular field at the rate of ` 3 per square metre is
` 1,728. If the breadth of the field is 18 m, find the cost of fencing the field at
` 8.5 per metre.

Solution: Area of the rectangular field = Total cost
Cost per square metre

1,728
= = 576 sq. m
3
Now, Length × Breadth = 576 sq. m

576
∴ Length of the field = = 32 m
18
Perimeter of the field = 2(l + b)
= 2(32 + 18) = 100 m
Cost of fencing the field = ` 8.5 × 100 = ` 850
Example 21: Split the following shapes into rectangles and squares and find their areas. (The
measures are given in centimetres).
2 2 4
4 4
3 3
3 4 4
8 8 4 4
3
3 3 4 4 4 4

2 2 4
(a) (b)

2 2
Solution: (a) Area of Fig. I (rectangle) = 8 cm × 2 cm = 16 sq. cm
3 3 3 Area of Fig. II (rectangle) = 8 cm × 2 cm = 16 sq. cm
8 I III II 8 Area of Fig. III (rectangle) = 3 cm × 2 cm = 6 sq. cm
3 Area of complete figure = (16 + 16 + 6) sq. cm = 38 sq. cm
3 3
2 2
4
4 4
(b) 4 II 4 Area of Fig. I (square) = 4 cm × 4 cm = 16 sq. cm
Area of 5 such figures = 5 cm × 16 cm = 80 sq. cm
4 I III V 4

4 4
4 IV 4
4
Example 22: A room measuring 7 m by 6 m is to be covered by square tiles of side 50 cm. Find
the number of tiles required to cover the floor. If the cost of one tile is ` 60, find the
total cost of tiles?
Solution: Area of the floor = Length × Breadth
= 7 m × 6 m = 42 sq. m
Area of each tile = Side × Side
= 0.5 m × 0.5 m = 0.25 sq. m

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