Take a sheet of A4 paper.  First fold the top left corner to meet the bottom edge and press the fold flat. Then fold the top right corner to meet the edge that you folded down.

Can you prove that the quadrilateral you have made is a kite?

Can you find the perimeter of the kite?

Use the length of the shorter edge as the unit. Then the length of the longer edge is $$\sqrt{2}$$ because the lengths of the edges of A4 paper are in the ration 1 : $$\sqrt{2}$$ .