SOLUTION: Prove the following theorem: If the diagonals of a convex quadrilateral are perpendicular to each other, then the area of the quadrilateral equals one-half the product of the leng

Algebra ->  Geometry-proofs -> SOLUTION: Prove the following theorem: If the diagonals of a convex quadrilateral are perpendicular to each other, then the area of the quadrilateral equals one-half the product of the leng      Log On


   



Question 711330: Prove the following theorem:
If the diagonals of a convex quadrilateral are perpendicular to each other, then the area of the quadrilateral equals one-half the product of the lengths of the diagonals

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Break up the quadrilateral into 4 right triangles. Find the area of each right triangle using the formula A = (b*h)/2 and then add up the individual areas to get the overall area for the quadrilateral.