Page 229 - ICSE Math 6

Now, perimeter of rectangle = 2(l + b)
= 2(5 m + 29 m) = 68 m
Thus, the length of a wire required to fence the plot is 68 m.

Example 19: A rectangular tabletop is of measure 10 cm by 6 cm. Another tabletop is square in shape
with side 8 cm. Do they have the same perimeter and the same area?
Solution: Perimeter of rectangular table top = 2(l + b)

= 2(10 + 6) cm = 32 cm
Perimeter of square shaped table top = 4 × side
= 4 × 8 cm = 32 cm
Clearly, they have the same perimeter.

Area of rectangular tabletop = l × b
= 10 cm × 6 cm = 60 cm 2
Area of tabletop which is square in shape = (length of side) 2
2
= (8 cm) = 64 cm 2
The area of the tabletop which is square in shape is more than the area of rectangular
tabletop.

Two figures with the same perimeter may or may not have the same area.

Example 20: A square and a rectangle have equal areas. If each side of the square is 15 cm and the
breadth of the rectangle is 25 cm, compare their perimeters.
Solution: Perimeter of square = 4 × side
= 4 × 15 cm = 60 cm
Area of a square = (length of a side) 2
2
= (15 cm) = 225 cm 2
Area of rectangle = length × breadth
Area of rectangle
⇒ Length of rectangle = Breadth of rectangle

225 cm 2
= 25 cm ( Area of square = Area of rectangle)

= 9 cm
\ Perimeter of rectangle = 2(l + b)
= 2(9 + 25) cm = 68 cm

Thus, the perimeter of rectangle is more than that of the square.

Two figures having the same area may or may not have the same perimeter.

Example 21: A rectangular floor has dimension 9 m by 7 m. If a square carpet of side 5 m is laid on
the floor, then what is the area of the floor which is not carpeted?

Solution: Area of rectangular floor = 9 m × 7 m = 63 m 2
Area of square carpet = 5 m × 5 m = 25 m 2
2
2
\ Area of the floor which is not carpeted = 63 m – 25 m = 38 m 2
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