How many different shapes can I draw with an area of (usinh 2 components)...

[icarusbop]

Hello:

My daugther has homework, part of which is as follows:
There are two shapes:
a = a square
b = a quarter circle.

The question posed is:
"How many different shapes can I draw with an area of 3a + 2b?" (There are different quantities to substitute here e.g. 5a+b...)

We have spent hours on this and still are no closer, we even made the shapes from paper and tried moving them around, but soon lost track of which shapes we had already made - my imediate suspicion is hundreds! Can anyone let me know how to calculatre this please? - I assume there is a simple formula of which I am not aware.

Regards

Ian

 

[Ishuda]

Hello:

My daugther has homework, part of which is as follows:
There are two shapes:
a = a square
b = a quarter circle.

The question posed is:
"How many different shapes can I draw with an area of 3a + 2b?" (There are different quantities to substitute here e.g. 5a+b...)

We have spent hours on this and still are no closer, we even made the shapes from paper and tried moving them around, but soon lost track of which shapes we had already made - my imediate suspicion is hundreds! Can anyone let me know how to calculatre this please? - I assume there is a simple formula of which I am not aware.

Regards

Ian

Unless there are some other restrictions, the are an infinite number of shapes. Take the 3a+2b area for example. Draw a rectangle x high and a base of 2b/x so that the area of the rectangle is 2b. On top of that draw a triangle with the base of 2b/x and a height of 3ax/b so that the area of the triangle is 3a. The total area is 3a+2b.

 

[icarusbop]

Thanks for the responses so far.

What grade is your daughter in?

Is what you posted the FULL original problem?

My daughter is 11 so she is in (UK) year 7 of school, so not that high on maths yet. This is homework set by the Secondary school she is about to start.

Unless there are some other restrictions, the are an infinite number of shapes. Take the 3a+2b area for example. Draw a rectangle x high and a base of 2b/x so that the area of the rectangle is 2b. On top of that draw a triangle with the base of 2b/x and a height of 3ax/b so that the area of the triangle is 3a. The total area is 3a+2b.

The only other information I can see as relevant is the two shapes a and b have the same length flat edges, that is - b could have started the same size and shape as a, then someone cut off one of the corners to make it into a quarter circle shape.
The two shapes have to stay in one piece and the same shape (we can't get one of the squares and shop it into two triangles for example), so we made them out of paper (in the first example 5 same size squares, then chopped the corner off two to make the quarter circles). Then we were re-arranging them into different shapes, on squared paper, but lost track of which patterns we had already made.

Ian

 

[icarusbop]

Thanks for the responses so far.

What grade is your daughter in?

Is what you posted the FULL original problem?

My daughter is 11 so she is in (UK) year 7 of school, so not that high on maths yet. This is homework set by the Secondary school she is about to start.

Unless there are some other restrictions, the are an infinite number of shapes. Take the 3a+2b area for example. Draw a rectangle x high and a base of 2b/x so that the area of the rectangle is 2b. On top of that draw a triangle with the base of 2b/x and a height of 3ax/b so that the area of the triangle is 3a. The total area is 3a+2b.

The only other information I can see as relevant is the two shapes a and b have the same length flat edges, that is - b could have started the same size and shape as a, then someone cut off one of the corners to make it into a quarter circle shape.