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Mensuration

Look at the following closed figures.

All of the above figures occupy some region or flat surface. The amount of flat surface or region occupied by a closed figure is known as the area of the closed figure.

Can we tell which one of the above three figures occupy a greater area?

We can answer this question, if we calculate the area of each figure. Now, how can we do so?

To calculate the area of each closed figure, we follow the below given steps.

Step 1: Firstly, we place the closed figure on a squared paper or a graph paper where every square measures 1 cm × 1 cm.

Step 2: Then we make an outline of the figure.

Step 3: Now we look at the squares enclosed by the figure. Some of them are completely enclosed, some half, some less than half and some more than half. Note down the number of squares of each category.

Step 4: Calculate the area of the closed figure by considering the following points.

(a) Takethe area of 1 full square as 1 square unit.

(b) Ignore portions of the area that are less than half a square.

(c) If some portion enclosed by the figure is more than half a square, then

count its area as one square unit.

(d) If exactly half of the square is counted, take its area as square unit.

Such a convention gives a fair estimate of the desired area.

Let us calculate the area of each figure using the above method and try to find out the figure whose area is more than the other two figures. So go through the given videos to understand the method.

For figure I

For figure II

For Figure III

From the above calculations, we can say that figure III has more area than others.

Thus, figure III occupies more space than others.

Let us now discuss one more example based on the area of closed figures.

Example:

Find the areas of the following figures by counting the squares.

Solution:

(a) The number of completely-filled and half-filled squares for the given figure is 14 and 2 respectively.

Therefore, area covered by fully-filled squares = (14 × 1) square units = ...

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