Area of quadrilateral with perpendicular diagonals

Author:
fredekr
Area of quadrilateral with perpendicular diagonals
The formula for the area of a quadrilateral with perpendicular diagonals is . Can you see why this is? Hint: Note that the lengths of the diagonals of the pink quadrilateral ABCD are equal to the lengths of the height and width of the green rectangle EFGH. Look at the area of the green rectangle. Compare it to the area of the pink quadrilateral by looking at the four pairs of pink and green triangles.