Page 138 - Maths Skills - 7

136 Maths

2. Find the area of the rectangle whose length and breadth are as follows.

(i) 4.5 cm, 5 cm (ii) 7 dm, 6.3 dm (iii) 4.6 m, 8 m
3. The length of the diagonal of a square is 82 cm. Find the length of its side and also the area of the
square.
4. Find the side of a square having area 3600 sq metre.

5. The sides of a park are in the ratio 4 : 3. If its area is 1728 m , find the cost of fencing it at the rate of
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` 3 per metre.
6. A rectangular floor has dimensions 125 cm × 250 cm. Find the total number of square tiles of 5 cm
required to cover the floor.

7. Find the length of the diagonal of a room having dimensions 8 cm, 6 cm and 10 cm as length, breadth
and height respectively.

8. Find the length of the longest rod that can be fitted into a cuboid having dimensions 1 m, 0.5 m and
0.75 m as length, breadth and height respectively.
9. The area of a rectangle is equal to the area of five similar squares. If the area of the rectangle is 125 m ,
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then find the length of each side of a square.
10. If a square of side 10 cm is folded into two equal halves, then find the area of the rectangle formed.

11. Find the cost of whitewashing of the room of dimensions 15 m × 12 m × 10 m at the rate of ` 2.50 per m .
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AREAS OF RECTANGULAR PATHS
Let us learn to find the areas of rectangular paths made around (inside or outside) a rectangle. And also we shall
learn to find areas of central paths, simply by using the formulae of rectangles and squares.

Let’s Attempt

Example 1: A carpet measures 25 m by 20 m. A border of width 50 cm is printed
along its sides. Find the cost of printing the border at ` 20 per m .
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Solution: In Fig., let rectangle ABCD be the carpet and the shaded region
represents the printed border.

AB = 25 m, BC = 20 m
Area of the rectangle ABCD = 25 m × 20 m = 500 m 2
PQ = 25 m – (0.5 m + 0.5 m) = 24 m
and QR = 20 m – (0.5 m + 0.5 m) = 19 m

Area of the rectangle PQRS = 24 m × 19 m = 456 m 2
Area of the border = Area of rectangle ABCD – Area of rectangle PQRS
= (500 – 456) m = 44 m 2
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\ Cost of printing the border = ` 20 × 44 = ` 880
Example 2: A rectangular lawn measuring 40 m by 20 m is surrounded by a path which is 3 m wide. Find the
area of the path.
Solution: Let ABCD be the lawn and shaded region shows the path around the lawn (Fig.).
AB = 40 m, BC = 20 m
Area of the rectangle ABCD = 40 m × 20 m = 800 m 2