Page 178 - Ganit Kaushal

Ex 8. Draw a rectangle of size 12 units × 8 units. What are the dimensions of another rectangle that can be
drawn inside it, without touching the outer rectangle that occupies exactly half of its area? (NCERT)
Sol. Area of the given rectangle = 12 units × 8 units = 96 sq units. Half of its area 12 units
= 48 sq units. Possible dimensions of a rectangle with area 48 sq units are 8 units
48 units × 1 unit; 24 units × 2 units; 16 units × 3 units; 12 units × 4 units;
8 units × 6 units. Out of these dimensions, only a (6 units × 8 units) rectangle 8 units 6 units
can be drawn inside the rectangle with dimensions (8 units × 12 units) without
touching its sides, as shown in the adjoining figure.

Ex 9. Shape A has an area of 18 square units, and Shape B has an area of 20 square units. Shape A has a
longer perimeter than Shape B. Draw two such shapes satisfying the given conditions. (NCERT)

Sol. (a) Shape A: Take a rectangle with dimensions (9 × 2) units, then its area = 18 sq units.
Its perimeter = 2(9 + 2) units = 22 units
Shape B: Take a rectangle with dimensions (5 × 4) units, then its area = 20 sq units.
Its perimeter = 2(5 + 4) units = 18 units
\ Shape A has a longer perimeter than shape B. 2 units 9 units 4 units
(b) Shape A: Take a rectangle with dimensions (18 × 1) units, Shape A 5 units
then its area = 18 sq units and its perimeter = 2(18 + 1) units = 38 units Shape B
Shape B: Take a rectangle with dimensions (10 × 2) units, then its area = 20 sq units.

Its perimeter = 2(10 + 2) units = 24 units
\ Shape A has a longer perimeter than Shape B.
[Students are advised to draw two similar shapes for case (b) as given for case (a)]
Ex 10. By splitting the following figures into rectangles, find 3 1
their areas (the measures are given in centimetres).
(NCERT) 2
2
5
4
4
3 3 3
2

3 1 1
(a) (b)
Sol. (a) The complete figure is divided into four rectangles, as shown in the figure. D A
Area of rectangle ABCD = 4 cm × 2 cm = 8 cm 2 F 3 1 E
Area of rectangle EFJC = 3 cm × (2 + 1) cm = 3 cm × 3 cm 2 4
= 9 cm 2 H 2 G
Area of rectangle GHIJ = 2 cm × 1 cm = 2 cm 2 1 B 1 K
Area of rectangle IKLM = 3 cm × (2 + 1) cm = 3 cm × 3 cm I J C B
= 9 cm 2 3 3
2
2
Hence, the total area of the figure = (8 + 9 + 2 + 9) cm = 28 cm . M L
(b) The complete figure is divided into three rectangles, as shown in the figure.
Area of rectangle ABCD = 3 cm × 1 cm = 3 cm 2 A B 5 E F
Area of rectangle EFGH = 3 cm × 1 cm = 3 cm 2 3 J 3 I
Area of rectangle BEIJ = {5 – (1 + 1)} cm × 1 cm = 3 cm × 1 cm = 3 cm 2 2 2
2
Hence, the total area of the figure = (3 + 3 + 3) cm = 9 cm 2 D 1 C H 1 G

176 Mathematics-6