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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

10. The length and breadth of a rectangular hall are 65 m and 45 m, respectively. Find
the cost of flooring it at the rate of `30 per sq. m.

11. The floor of a rectangular room is 5 metres long and 4 metres wide. A square carpet
with a side of 3 metres is placed in the centre of the room. What is the area of the
floor that is not covered by the carpet?

AreA of irregUlAr ShApeS

Let us find the area of the adjoining figure.

To find the area of closed figures on square grid paper, we follow the given steps:
Step 1: Count the number of squares of unit length which are completely enclosed by the
figure. In the figure, number of complete squares, m = 55.

Step 2: Count the number of squares of unit length of which more than half is enclosed
by the closed figure.
Here, number of more than half squares, n = 8.

Step 3: Count the number of those squares of which
exactly half is enclosed by the figure and divide the
number by 2.

Number of half squares, p = 5.
Step 4: Ignore those squares of which less than half is
enclosed by the figure.
Step 5: Add the total squares of steps 1, 2 and 3 to obtain

the area of the complete figure.
Thus, Area of the irregular closed figure = Number of complete squares (m) +
1
Number of squares more than half enclosed (n) + × Number of squares half
enclosed (p). 2
1
= 55 × 1 sq. units + 8 sq. units + × 5 sq. units
2
= 55 sq. units + 8 sq. units + 2.5 sq. units
= 65.5 sq. units.

1
Generally, area of the irregular closed figure = (m + n + p) sq. units.
2
We use this method to find the area of irregular figures.

maths fun
Experiential Learning
Take a square grid paper of 1 cm × 1 cm unit squares and trace your
palm on it. Calculate the area enclosed by your hand.

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Mathematics-5
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