# Rectangles of certain Area fitting into larger rectangle of certain dimensions

I have an issue where I need to do the following:

Smaller rectangles (e.g., any size, but must have Area = 100 sq. ft.) must fit within another, larger rectangle (e.g., dimensions = 400 x 600 feet) with 4 columns and 6 rows (thus, 24 smaller rectangles fitting within).

I need to be able to see what sizes of the smaller rectangles meet the Area requirements and fit within the larger rectangle.

Obviously, 10 x 10 is the simplest option with the above examples, but I would like to use multiple differently-sized smaller rectangles.

I have tried to use Excel to choose lengths and widths of the smaller rectangles (i.e., trial and error), but this seems very inefficient.

Can anyone please help me come up with an algorithm to test something like this or suggest software which would be helpful to figure this out?

Thank you.

• Look into "rectangle packing algorithm"s Jan 14 at 22:39
• When you say rows and columns, is it a grid, with the rows cutting all the way across, and the columns all the way down? Or is it more loose, like 6 rows with 4 rectangles each but they don't have to line up with each other? Jan 15 at 2:04