Show that if the diagonals of a quadrilateral are perpendicular, then its area is half the product of the diagonals.

Question

What kind of drawing do I do? And how doI solve this? Thank you!

Answer 1

Draw a long line, mark a point O on the line
mark one side of O length a
mark the other side length b
the total length is then (a+b)
Draw a short line through O perpendicular to the first one

Draw a short line through O, perpendicular to the long one .
Lengths c and d, total length (c+d)

Those are your two diagonals.
now connect the tips of those lines and you have your quadrilateral.

Now look at the four triangles
area is
(1/2)ac + (1/2)ad + (1/2)bc + (1/2)bd

now what is (1/2)(a+b)(c+d) ?
(1/2)( ac + ad + bc + bd)

:) look familiar?