Question

2. Make a grid on paper with square size of 1 cm by 1 cm. Very carefully trace
the outline of your hand on it. Estimate the area covered by your hand by adding the
whole covered squares with those that are covered more than half. Compare the
outline of your hand with any one of your family member.
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Answer 1

Step-by-step explanation:

Draw a big square around your hand. This is your 1st generation square. Calculate it’s area.

Divide it into 4 equal squares. These will be your 2nd generation squares.

Divide those new 4 squares into 16 new squares to generate 3rd generation.

Repeat this process 3–4 times more for each square residing on the boundary of your hand to create next generation of squares.

This process should look something like this:

Now, count how many last generation squares reside on the boundary of your hand, and divide this number by 2. Notice that approximately half of their areas reside inside your hand, and the other half reside outside, that’s why we divide it by 2.

Next, count how many last generation squares reside inside your hand, and add previous number to this number.

Then, count how many parents of the previous generation squares reside inside your hand. Divide the previous number by 4, and add it to this number. Parent squares are 4 times bigger than their child squares, that’s why we divide the previous number by 4.

Repeat the previous step till you reach the 1st generation.

You’ll end up with a number smaller than 1, and that number is the ratio of the area of your hand to the area of the 1st generation square.

Multiply that number with the area of the 1st generation square, and you’ll get the area of your hand.

Increase the number of square generations to get more accurate results. You’ll be surprised how accurate it gets even after 4–5 generations

Answer 2

Step-by-step explanation:

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