Dividing a 5-Square Cross into 4 Equal Squares

In summary, the conversation discusses a figure consisting of five equal squares arranged in the form of a cross and the challenge of dividing it into four equal parts that can fit together to form a square. The concept of "equal" is questioned and a solution is proposed, with a link to an image for reference. One participant acknowledges an error in their solution and expresses dissatisfaction with its removal without notification.
  • #1
vaishakh
334
0
A figure contains five equal squares in the form of a cross. Can you show how to divide this figure into four equal parts which will fit together to form a square
 
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  • #2
By "equal" do you mean "congruent" or "equal in area"?
 
  • #3
Tricky. If the five original squares are unit squares, then the area of the square you have to form from them is 5. So the sides would have to be sqrt(5) long = 2.236 approximately. Here's a way you might do it - but the diagram isn't to scale.
 

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  • #4
I posted the solution to this the other day but for some reason it has been removed, here it is again, not sure if it is the same as Ceptimus' as his attatchment is still pending.
 
  • #5
The question said 'four equal parts'. Joffe's disection is ingenious, but the parts aren't equal.

As my attachment approval is still pending, here is a link to the same image hosted elsewhere.

http://www.mround.pwp.blueyonder.co.uk/physics/image/disection.gif [Broken]
 
Last edited by a moderator:
  • #6
Aha, I didn't read the question carefully enough, thanks for pointing that out Ceptimus. Whichever moderator deleted I think should have instead pointed out my error or at least PM'd me, rather rude I feel.
 

1. How can a 5-square cross be divided into 4 equal squares?

To divide a 5-square cross into 4 equal squares, you can start by drawing a vertical line through the center of the cross, dividing it into two rectangles. Then, draw a horizontal line through the center of the top rectangle, dividing it into two squares. Repeat this process on the bottom rectangle to create a total of 4 equal squares.

2. Is it possible to divide a 5-square cross into 4 equal squares without any overlapping?

Yes, it is possible to divide a 5-square cross into 4 equal squares without any overlapping. This can be achieved by following the method described in the answer to the previous question.

3. Can I divide a 5-square cross into 4 equal squares using different methods?

Yes, there are multiple ways to divide a 5-square cross into 4 equal squares. Some other methods include drawing diagonal lines through the cross, creating 4 smaller crosses, or using geometric constructions such as the "Greek cross" method.

4. Why is it important to divide a 5-square cross into 4 equal squares?

Dividing a 5-square cross into 4 equal squares can be important for various reasons. It can be used as a visual aid for teaching concepts in geometry, or it can be used in problem-solving tasks and puzzles. Additionally, dividing shapes into equal parts can help improve spatial awareness and critical thinking skills.

5. Can this concept be applied to other shapes?

Yes, this concept can be applied to other shapes as well. Any shape with an equal number of sides can be divided into equal parts using similar methods. However, the specific steps may vary depending on the shape and the number of equal parts desired.

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