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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 Mathematics

User Lashgar
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Answer:

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

Step-by-step explanation: So the answer is 12 square units

User Redek
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8.1k points
3 votes
We are asked to solve for the area of the trapezoid and the formula in the is shown below:
Area = (a+b)/2 *h where a & b are the bases and "h" is for the height

We have the given values:
a = x units
b =y units
h = z units

Area = (x+y)/2 *h
User Mikegrb
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8.7k points

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