By studying this lesson, you will be able to,
● identify the amount of space occupied by a surface as its area,
● measure the area using arbitrary units,
● recognize cm2 as a unit of measurement of area,
● measure the areas of squares and rectangles using a 1 cm × 1 cm square grid and
● create figures of given area using 1 cm2 square laminas.
The space allocated for six students to display their creations on a wall newspaper is shown in the figure.
The space allocated to each student can be identified as a surface which is bounded by line segments. The space occupied by a surface is known as its area.
Observe the amount of space each student has been allocated.
We can easily say that the space allocated to Kavindu on the wall newspaper is more than the space allocated to Akila because both have been allocated similar shaped spaces.
That is, Kavindu has been allocated a space with a larger area than the area of the space Akila has been allocated.
Step 1 - Cut out a square shaped lamina of side length 6 cm from a piece of cardboard.
Step 2 - By taking the area of the lamina to be 1 unit, determine how many units the area of the following surfaces are by placing the lamina on each of them.
1. The front page of your mathematics textbook.
2. The front page of your mathematics exercise book.
3. The top surface of your desk.
Step 3 - Cut out a rectangular shaped lamina of length 8 cm and breadth 3 cm from a piece of cardboard.
Step 4 - As before, find the area of the above surfaces using this lamina.
The figure illustrates how a student has placed a rectangular shaped lamina on a page of his mathematics exercise book to determine the area of the lamina.
Let us take the area of the square which has been shaded in red as one unit. Then the area of the rectangular lamina is 24 of these units.
This figure illustrates how another student has placed the same rectangular lamina on a new square grid of a different size to find its area.
Let us take the area of the square which is shaded green as 1 unit. Then the area of the rectangular lamina is 6 of these units.
Two values which are numerically different to each other and which depend on the unit that has been used, are obtained for the area of one and the same rectangular lamina, namely 24 units of the red square and 6 units of the green square. Therefore, when the area is given, the unit used to measure the area too has to be mentioned.
(2) Find the area of each of the following figures which have been drawn on a 1 cm × 1 cm square grid.
