Area of trapezium Question ? =) ( also part of coordinate geo :P)?

Question

A trapezium has vertices H (0,0) , I(0,12) , J (9,12) and K (16,0).

Place these on a number plane and answer question :

Explain why the area of this trapezium equals half the product of the diagonal lengths ?

Huh ? =S

Answer 1

Draw the trapezium,then find the areas of the rectangle and triangle,add them up.

Answer 2

Let parallel sides be a and b

h = perpendicular height

A = 1/2 (a + b ) h

A = (1/2) (16 + 9) 12

A = 150 units ²

Let diagonals be d1 and d2

d1² = 9² + 12²

d1² = 225

d1 = 15

d2² = 16² + 12²

d2² = 400

d2 = 20

(1/2) (d1) (d2) = (1/2) (15) (20) = 150 units ²

As required.