area for a fixed perimeter

you have a 32 unit long electro rope for enclosing animals
what areas can be enclosed?

oh, by the way, you need to know about a world famous right angled triangle

some suggest that the Ancient Egyptians may have used this triangle to construct right-angles
when building the pyramids

but
there seems little evidence for this view






students could explore the (given or discovered) areas of rectangles with a perimeter of 32

establish that the perimeters of these shapes are all 32

what are their areas?

question (8) needs a calculator (for the circle with a perimeter of 32)

what is a message from this work?