Page 186 - Ganit Kaushal

4. Assertion (A): Two rectangular sheets, each of length 20 m and width 10 m, are placed edge to edge
along their longer sides. The perimeter of the resulting figure is 80 m.
Reason (R): The perimeter of a regular pentagon is 5 times the length of a side.
5. Assertion (A): A mobile phone is 15 cm long and 8 cm wide. The sum of the areas of the front and
the back of the mobile phone is 240 sq cm.
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Reason (R): Area of a square with side ‘a’ is a .
6. Assertion (A): The dimensions of a paper strip are 6 cm by 1.5 cm. The total area of both sides of
six such paper strips is 108 sq cm.
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Reason (R): The area of one side of paper strip with dimensions 6 cm by 1.5 cm is 9 cm .
7. Assertion (A): The length of a hall is 40 metres and its width is half of its length. Therefore, the
perimeter of the hall is three times its length.
Reason (R): Area is measured in square units.
Case Study Based Questions
Rohit purchased a rectangular farmland of length 150 metres and breadth
100 metres. Based on this information, answer the following questions:

1. How much land has Rohit purchased?
2. He wants to stroll around the farmland. How much will he walk?
3. Rohit wants to put a fence using poles and wires, with three layers
of wire around the farmland, to prevent stray animals from entering.
How much wire will be needed?
4. If poles are placed along the boundary at a distance of 10 metres, how many poles are needed?

5. If the cost of wire is `30 per metre, poles cost `35 each, and the cost of labour is `8000, then how
much did the fencing cost Rohit?
6. Rohit decided to construct a house for himself on 1 of the area of the farmland. What area of the
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farmland will be left for farming after constructing the house?
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7. The cost of land is `5000 per m . How much money did Rohit spend on the land? Give your answer
in the Indian system of numeration.

Summary of the Chapter

• The perimeter of a polygon is the sum of the lengths of all its sides.
(a) The perimeter of a rectangle is twice the sum of its length and width.
(b) The perimeter of a square is four times the length of any one of its sides.
(c) The perimeter of a regular polygon having ‘N’ sides is N times the length of any one of its sides.
• The area of a closed figure is the measure of the region enclosed by the figure.
• Area is generally measured in square units.
• The area of a rectangle is its length multiplied by its width. The area of a square is the length of any one
of its sides multiplied by itself.
• Two closed figures can have the same area with different perimeters, or the same perimeter but different
areas.
• Areas of regions can be estimated (or even determined exactly) by breaking up such regions into unit
squares, or into more general-shapes like rectangles and triangles, whose areas can be calculated.

184 Mathematics-6