ACTIVITY
Do the activity with a partner. One of you will perform the paper folding while the other will do the recording in table 1. Start with a big square from a piece of paper. Assume that the area of the square is 64 square units.
1. Fold the four corners to the center of the square and find the area of the resulting square.
2. Repeat the process three times and record the results in the table below.
Square
Area
1
2
3
Answer (1)
To solve this problem, you need to follow the process of folding a piece of paper and calculating the resulting area as described. Here is a step-by-step explanation:
Start with the Original Square :
The area of the original square is 64 square units. Since a square's area is calculated as the side length squared, each side of the original square is 64 = 8 units.
First Fold :
Fold the four corners of the square into the center. The new shape will result in another square.
When you fold the four corners to the center, the area of the resulting square is half of the original square. Therefore, the area becomes 2 1 × 64 = 32 square units.
Second Fold :
Repeat the process by folding the four corners of the new square. This process halves the area again.
The area after the second fold: 2 1 × 32 = 16 square units.
Third Fold :
Repeat the folding process a third time.
The area after the third fold: 2 1 × 16 = 8 square units.
Here's a summary of the areas recorded:
After the first fold: 32 square units
After the second fold: 16 square units
After the third fold: 8 square units
By following this method, you can see how the area of the square is reduced by folding the corners and how the area changes with each step.
