Begininning with a right triangle of sidesa,b, andc, (ais the hypotenuse,bis the base,cis the height) determine its area in two ways; by the standardA= (1/2)(base)(height) and by Heron's Formula. Equate these and manipulate the resulting, dreadful equation until you have derived the theorem of Pythagoras;a^2 =b^2 +c^2.

See attached for Heron's Formula

Attachment 19345