Page 189 - Ganit Kaushal

Activities

Activity 1: ‘Making It More or Less.’

For a given fixed area, we can make shapes with greater or smaller perimeters.
Make two adjoining figures with the help of a square grid paper sheet and
observe them. Both figures have an area of 9 sq units, but they have different
perimeters. The first figure has a perimeter of 12 units, and the second has a (i) (ii)
perimeter of 20 units.
Students are advised to arrange or draw different figures with 9 sq units to find other perimeters. 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.
Using 9-unit squares, try answering the following questions and discuss them with your classmates.

1. What is the smallest perimeter possible? 2. What is the largest perimeter possible?
3. Make a figure with a perimeter of 18 units.
4. Can you make other differently shaped figures for each of the above three perimeters, or is there
only one shape possible for each? What is your reasoning?
(Hints to answer the above questions are given at the end of this book in the answers section. Students
are advised not to see those in advance. Try to answer them at least once on your own.)

Activity 2: ‘Estimating the Area of Irregular Shapes’

Make any close irregular figure as shown and proceed as under:
1. Place the figure on a transparent squared grid paper sheet where
every square measures 1 unit × 1 unit.
2. Mark an outline of the figure on the squared paper as shown here.
3. Now, find the area using the conventions C1 ̶ C4 given in section
6.3 to estimate the area of irregular shapes in section 6.3 of this
chapter. Answer: 6 sq units.
 Students are advised to make more irregular shapes and estimate their area using C1 ̶ C4.

Activity 3: ‘Forming Rectangles of a Given Area’

Take a squared grid paper sheet where every square measures 1 unit × 1 unit.
1. Make as many rectangles as you can, such that the area of the
rectangle is 16 sq m. (Consider only natural number lengths.)
A case is shown in the adjoining figure. The perimeter of this rectangle
is 20 units. Similarly, find the perimeters of all the rectangles you draw
with an area of 16 square units and answer the following questions:
(a) What are the dimensions of the rectangle having the largest perimeter?
(b) What are the dimensions of the rectangle having the least perimeter?
2. Do the same for an area of 24 sq units and answer the same questions (a) and (b). Discuss your
answers with classmates.

187