Find the area of this quadrilateral with the given vertices:
A(-8,6) B(-5,8) C(-2,6) D(-5,0)
To find the area of a quadrilateral, you can use the Shoelace Formula, also known as the Gauss's area formula.
The Shoelace Formula states that if you have the coordinates of the vertices of a polygon listed in counterclockwise order (or clockwise, as long as you consistently follow the order), you can calculate the area by subtracting the sum of the products of the coordinates of the vertices below the main diagonal from the sum of the products of the coordinates of the vertices above the main diagonal, and then dividing the absolute value of this result by 2.
Let's calculate the area of the given quadrilateral using the Shoelace Formula:
1. Write the coordinates of the vertices in counterclockwise order:
A(-8,6), B(-5,8), C(-2,6), D(-5,0)
2. Multiply the x-coordinate of each vertex by the y-coordinate of the next vertex and add them together:
(-8 * 8) + (-5 * 6) + (-2 * 0) + (-5 * 6)
3. Multiply the y-coordinate of each vertex by the x-coordinate of the next vertex and subtract them from the previous result:
-64 - 30 + 0 - 30
4. Divide the absolute value of the result by 2 to get the area:
|(-64 - 30 + 0 - 30)| / 2 = |-124| / 2 = 124 / 2 = 62
Therefore, the area of the given quadrilateral is 62 square units.