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Infinitely many.

You can have a circle with a radius of approx 1.78 units.

Or, for any positive value of x,

an ellipse whose axes are x units and pi/(10*x) units in length,

a triangle whose base is x units and whose vertical height is 20/x units,

a parallelogram whose base is x units and whose vertical height is 10/x units.

And then there are polygons of 5, 6, sides and so on.

You can also combine a triangle with an area of 4 units with a semicircle with an area of 6 units and other weird and wonderful shapes.

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Q: How many shapes can you make with an area of 10 square units?
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Can you draw a rectangle that has an area of 5 square units and a perimeter of 12 units?

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How many shapes can you make with an area of 5 square units?

12Infinitely many all different:As it is only the area that matters, the perimeter can be any shape:An equilateral triangle (with sides approx 3.398 units)A square (with sides approx 2.236 units)A regular pentagon (with sides approx 1.705 units)A regular hexagon (with sides approx 1.387 units)A regular heptagonA regular octagonA regular nonagonA regular decagonA regular hendecagon (11 sided polygon)A regular dodecagon (12 sided polygon)A regular triskaidecagon (13 sided polygon)A regular 14 sided polygonA regular 15 sided polygonA regular 16 sided polygon...A circle (with radius approx 1.262 units)And there are also the non-regular shapes, eg an L shaped hexagon, a kite, a parallelogram which can have an area of 5 square units.


Is there a way to make a square using 6 shapes?

Yes, it is possible to make a square using six shapes, depending on the shapes used. For example, you could use four right triangles and two squares, arranging them so that the triangles fill in the corners of a larger square formed by the two squares. Alternatively, other combinations of shapes, such as rectangles or irregular polygons, can also be arranged to create a square. The key is to ensure that the total area and configuration of the shapes collectively form a perfect square.