Page 193 - Math_Genius_V1.0_C6_Flipbook

E:\Working\Focus_Learning\Math_Genius-6\Open_Files\09_Chapter_6\Chapter_6
\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

Quick Check
Which of the following figures has the greatest area?
First guess and then verify your estimate by actual calculation.
1. 2. 3.

Making Different Arrangements

During the maths period, the teacher divided the class into groups of three students each and
provided a square grid paper to each group. Then, she instructed each group to colour a certain
number of unit squares in different ways. Remember that each square should align with at least
one other square on at least one side completely and together all squares should form a single
connected figure with no holes.
A group of three students shows their working as shown below.

Think and Answer

1. If you shift a unit square to another
place in Rahul’s shading, what would be
the perimeter – increase or decrease?
2. Arrange or draw different figures with
16 sq. units to obtain various perimeters.
Seema’s Shading Nagma’s Shading Rahul’s Shading
What do you see in their shadings? Do they have the same perimeter and area?
We can see that each one has shaded 16 unit squares. So, their areas are the same.
But, their perimeters are not the same. As the perimeter of Seema’s shading is 16 units, Nagma’s
shading is 34 units and that of Rahul’s shading is 26 units.

Example 16: 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.

Solution: Given, shape A has an area of 18 square units and shape B has an area of 20 square units.
Therefore, shape A can be a rectangle with dimensions:

9 units × 2 units or 6 units × 3 units

I II
Perimeter of Ist shape = 2(9 + 2) = 2 × 11 Perimeter of IInd shape = 2(6 + 3) = 2 × 9
= 22 units = 18 units

191
191 P erimeter and Ar ea
Perimeter and Area