Session 8: Area of Irregular Shapes Using Squared Paper – Definition, Interactives and Examples

What is Area?

The area is the amount of surface enclosed by a closed two-dimensional figure. It is measured by the number of unit squares it takes to cover a two-dimensional shape. For example, if you count the small squares, you will find there are 15 of them. Therefore, the area is 3⋅5 or 15 unit².

---

Finding Area of Irregular Shapes Using Squared Paper

When a simple close figure is drawn on a squared sheet paper (paper made up of squares of sides 1 unit by 1 unit. The area of each of these squares is 1 unit² ), we can easily find the approximate area by counting the number of squares enclosed by the figure. This method helps find the area of irregular shapes.

In this method, make a traced copy of the figure on transparent paper, put it on squared paper, and count the number of squares inside the figure. For calculations of the approximate area, we count the number of squares that are completely enclosed or whose more than half the parts are enclosed by the figure as one. Count the squares whose exactly half parts are enclosed as ½ and leave out all the squares which are less than half in the figure.

Thus, the approximate area of shape = number of full and more than half squares + ½ (number of half squares)

---

Area of Irregular Shapes – Examples

Example 1

Find the approximate area of the given regular shape.

The number of complete squares enclosed = 8

The number of more than half squares enclosed = 4

The number of half squares enclosed = 0

Approximate area=

=12 unit²

Example 2

Find the approximate area of the given shape.

The number of complete squares enclosed = 6

The number of more than half squares enclosed = 6

The number of half squares enclosed = 1

Approximate area=

                              =\(12\frac{1}{2}\) unit²

Remember this!

• The approximate area of irregular shapes can be found using squared paper.
• We find the approximate area of irregular shapes in the following way:
  – We count the number of squares that are completely enclosed or whose more than half the parts are enclosed by the figure as one.
  – We count the squares whose exactly half parts are enclosed as \(\frac{1}{2}\)
  – We leave out all the squares which are less than half in the figure