This document explains how to find the area when increasing the length and breadth of a rectangle. It provides examples of: 1) Increasing the length of a 12 x 7 rectangle by 3cm, which results in a 15 x 9 rectangle with an area equal to the sum of (12 x 7), (12 x 2), (3 x 7), and (3 x 2). 2) Finding the area of a 14 x 16 rectangle from a 13 x 15 rectangle by writing it as (13+1) x (15+1) and distributing the factors. 3) The general formula for multiplying sums of positive numbers, which is to multiply each number in one sum by each number in the other sum and

2. AREA=12 X 7
7
12

3. Increasing its length by 3cm
12
7
3
(12+3) x
7
= (12 x
7)
+ (3 x 7)

4. Now suppose we increase
the length by 3cm and
breadth by 2cm

5. Now we increase the breadth in the original
rectangle by 2cm
12
7
2
Increase in area is
12 x(7+2)=(12 x 7)+(12 x 2)

6. 12
7
3
2

7. To make it a rectangle we need
a small rectangle
12
7
3
2 2
3

8. 12
7
3
2
3
2
AREA IS 15 X 9
15 X 9 =(12 X7)+(12X2)+(3X7)+(3X2)
(12+3)X(7+2) =(12 X7)+(12X2)+(3X7)+(3X2)

9. To get 15 x 9 from 12 x 7
•15 x9 is split as (12+3) x (7+2)
• 7 and 2 multiplied by 12
• 7 and 2 are multiplied by 3
•All these products were added

10. Find 14 x 16 from 13 x 15
14 x 16 = (13+1)(15+1)
=(13 x 15)+(13 x 1)+(1 x15)+(1 x

11. To multiply a sum of
positive numbers by a sum
of positive numbers
,multiply each number in
the second sum by each
number in the first sum
and add

12. FIND 26 X 74
26 X 74 =(20+6) X (70+4)
=(20 X70)+ (20 X 4) + (6 X70) +(6 X 4)
=1400+80+420+24
=1924

13. (x+y)(u +v) =xu+xv+yu+yv
for any four positive
numbers x,y,u,v