On a square handkerchief, nine circular designs each of radius 7 cm are made (see Fig. 12.29). Find the area of the remaining portion of the handkerchief.

Explanation

To find the area of the remaining portion of the handkerchief after making nine circular designs, we can follow these steps:

### Step 1: Calculate the area of the square handkerchief.
Let the side length of the square handkerchief be \( s \). Since there are nine circles arranged in a square formation, we can assume that the circles are arranged in a 3 by 3 grid. The diameter of each circle is \( 2 \times 7 \, \text{cm} = 14 \, \text{cm} \).

Thus, the side length of the square handkerchief can be calculated as:
\[
s = 3 \times \text{diameter of one circle} = 3 \times 14 \, \text{cm} = 42 \, \text{cm}
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