LEARNATHON

III

Competition for grade 6 to 10 students! Learn, solve tests and earn prizes!

Learn more### Theory:

Have you ever noticed the shape of the leaves, route maps, feather of birds or flowers?

All these objects will have irregular shapes and sizes.

There is no way to calculate the area of these irregular figures using a formula. Then, which method can be used to determine the area of an irregular object?

The answer is 'Graphical method'.

Area of irregularly shaped plane figures

**Graphical method**

This method requires a leaf, a graph sheet and a pencil.

**Procedure**

- Look around your neighbourhood and pick a leaf from a tree.
- Take a graph sheet and place the leaf on it.
- Outline of the leaf using a pencil on the graph sheet.
- Now, remove the leaf and notice the outline.

**Calculation**

- First, count the complete squares that are contained within the leaf's outline. Note it as \(A\).
- Then, count the squares that are greater than half, assume it as \(B\).
- Now, count the squares that are half the size of a whole square. Take it as \(C\).
- Finally, count the squares that are less than the size of the full square. Take it as \(D\).

**Formula**

The formula to calculate the approximate area of the leaf is,

$\mathit{Area}\mathit{of}\mathit{the}\mathit{leaf}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}A+\left(\frac{3}{4}\right)\phantom{\rule{0.147em}{0ex}}B+\left(\frac{1}{2}\right)\phantom{\rule{0.147em}{0ex}}C+\left(\frac{1}{4}\right)\phantom{\rule{0.147em}{0ex}}D\phantom{\rule{0.147em}{0ex}}{\mathit{cm}}^{2}$

The approximate area of irregularly shaped plane figures can be calculated using the above formula.

We can also use a graphical method to find the area of the regularly shaped figures like square, rectangle, triangle, and circle. This method gives us an accurate area, especially for square and rectangle.