Page 172 - Ganit Kaushal

Solved Examples

Ex 1. Find the area of the following figures using conventional rules. (NCERT)

(a) (b) (c) (d)
Sol. Applying the above conventional rules, we have:

(a) (b) (c) (d)
1 1
(a) Area of the figure = + 1 + 1 + 1 + = 4 sq units. (Count green and red dots)
2 2
1 1 1 1 1 1
(b) Area of the figure = + + + + 1 + 1 + 1 + 1 + + 1 + 1 + = 9 sq units.
2 2 2 2 2 2
(Count green and red dots)
1 1 1 1 1 1
(c) Area of the figure = + + 1 + 1 + + 1 + 1 + 1 + + 1 + 1 + + = 10 sq units.
2 2 2 2 2 2
(Count green and red dots)
1 1 1 1 1 1
(d) Area of the figure = 1 + 1 + 1 + 1 + + + + + + + 1 + 1 + 1 + 1 = 11 sq units.
2
2
2
2
2
2
(Count green and red dots)
Ex 2. On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can whose lengths
and widths are a whole number of units such that the area of the rectangle is 24 square units.
(a) Which rectangle has the greatest perimeter?
(b) Which rectangle has the least perimeter?
(c) If you take a rectangle of area 32 sq units, what will your answers be? (NCERT)
Sol. Using factorisation, we can write 24 as: 24 = 1 × 24; 24 = 2 × 12; 24 = 4 × 6; 24 = 8 × 3

Taking 24 = 1 × 24, we get a rectangle whose length (l) is 24 units and breadth (b) is 1 unit.
24 units
1 unit

\ Its perimeter = 2(l + b) = 2 (24 + 1) = 50 units. Similarly for other pairs.
6 units
If 24 = 2 × 12, then the perimeter of the rectangle is 28 units.
If 24 = 4 × 6, then the perimeter of the rectangle is 20 units. 4 units
If 24 = 3 × 8, then the perimeter of the rectangle is 22 units.

170 Mathematics-6