Mathematics
beamoreno
29

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

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(1) Answers
jfivnckx

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

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