Area = 10 Challenge

Find as many as possible different (non-congruent) rectangles on square grid paper so: • The corner of each rectangle touches the intersections of grid points and • The area of each rectangle is 10 square units See if you can find all solutions. Can you prove that these are the only possible solutions?
Extension questions Try the problem but this time, change the area to 11 or 12 or 9… etc… What area gives the most solution to the problem? Is there any pattern(s)?