Trapezoid abcd is graphed in a coordinate plane.

what is the area of the trapezoid?

10 square units
12 square units
20 square units
24 square units

In geometry we are taught to find the area of a shape by a given formula. For example, the trapezoid shown in the figure has a formula for area of

A = 1/2 *((base 1 + base 2)/2)*height

But for polygons drawn on a Cartesian plane with known coordinates, the formula for area is

A = 1/2 * determinant

The determinant refers to the determinant of the matrix of coordinates. It is a two-column matrix, wherein the first column is the x-coordinate and the second is the y-coordinate. Just make sure that the points are arranged such that they are adjacent with each other. The matrix for this would be
  
    -5   -2   <---- point A
    -1    2   <---- point B
     0   -1   <---- point C
     -2  -3   <---- point D
    -5   -2   <---- point A

Just cross multiply the coordinate with a pattern shown in the picture. Don't mind the numbers. Focus on the pattern for determining the matrix. In this case,

Area = 1/2 * [(-10-2)+(1-0)+(0-2)+(4-15)]
Area = 12 square units

The answer below is correct, the answer is 12.

For those of you who do not believe me, putting in 24 is going to give you a  wrong answer, it happened to me