Page 171 - Ganit Kaushal

Estimating the Area of Irregular Figures using Conventional Rules

Look at the figures alongside: (i) and (ii).
Can you answer which one has a greater area?

Again, it is difficult to find the area of these figures by only
observation. Also, these figures are shaped in such a way that
they do not fit into complete squares, as in the case above.
What can we do now to overcome such a problem?

No problem! Place them on a square grid paper and (i) (ii)
follow the ‘Conventional Rules’ C1 – C4 given below:
C1. The area of one full small square is taken as 1 sq unit.
C2. If more than half of a square is in a region, count it also as 1 sq unit.
1
C3. If exactly half of a square is in a region, count it as    sq unit.
2

C4. Ignore portions of the area that are less than half a square.
Now, we put the above figures on square grid paper sheets. For convenience in counting the three types of
squares, we mark full squares with a green dot (•) or tick ( ), more than half squares with blue dots (•) or cross
( ) and exactly half squares with red dots (•) or @ sign; the rest will be ignored. This gives us the adjoining
figures (i) and (ii).

Now, following the conventions C1 – C4, we can find the area of these two figures as follows:
Area of Fig. (i)

Number of complete squares (green dots) = 16
Number of more than half squares (blue dots) = 6

Number of exactly half squares (red dots) = 8

The rest are ignored.
1
So, area of Fig. (i) = 16 + 6 + (8) = 16 + 6 + 4 = 26 sq. units (i)
2
Area of Fig. (ii)

Number of complete squares (marked ) = 16

Number of more than half squares (marked ) = 9
Number of exactly half squares (marked @) = 4, and the rest are ignored.

1
So, area of Fig. (ii) = 16 + 9 + (4) = 16 + 9 + 2 = 27 sq. units
2 (ii)
Thus, we can say that Fig. (i) has less area than Fig. (ii).

Note

Students need to be very vigilant while doing this, because even a little more than half a square is considered
as full, and a little less than half is ignored.

Perimeter and Area 169