How do you find the area of a trapezoid using coordinates?

Answer 1

List the ordered pairs for the vertices in counterclockwise order, repeating the first ordered pair at the bottom of the list.

Find D, the sum of the downward diagonal products (from left to right.)

Find U, the sum of the upward diagonal products (from left to right.)

Use the formula A=1/2(D-U) to find the area.

This works for any closed polygon.

Example: Consider the trapezoid bounded by the points, (0, 0), (1, 2), (4, 2), and (4, 0). Write the list:

(0, 0)

(4, 0)

(4, 2)

(1, 2)

(0, 0)

Find D = 0*0 + 4*2 + 4*2 + 1*0 = 16

Find U = 4*0 + 4*0 + 1*2 + 0*2 = 2

Find A = 1/2 (D-U) = 1/2(16-2) = 1/2(14) = 7sq units