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 given its vertices, we can use the shoelace formula. The formula involves calculating the sum of the products of the coordinates of consecutive vertices, and then subtracting the sum of the products of the coordinates of consecutive vertices in the opposite order.
Here are the steps to find the area using the shoelace formula:
Step 1: Write down the coordinates of the given vertices:
A(-8, 6), B(-5, 8), C(-2, 6), D(-5, 0)
Step 2: Use the coordinates to calculate the products of consecutive x and y values:
A: (-8 * 8) = -64
B: (-5 * 6) = -30
C: (-2 * 0) = 0
D: (-5 * 6) = -30
Step 3: Add up the products of the x values:
-64 + (-30) + 0 + (-30) = -124
Step 4: Use the coordinates to calculate the products of consecutive y and x values:
A: (6 * -5) = -30
B: (8 * -2) = -16
C: (6 * -5) = -30
D: (0 * -8) = 0
Step 5: Add up the products of the y values:
-30 + (-16) + (-30) + 0 = -76
Step 6: Calculate the absolute value of the difference between the two sums:
|(-124) - (-76)| = |-124 + 76| = |-48| = 48
Step 7: Divide the absolute value by 2 to find the area of the quadrilateral:
48 / 2 = 24
Therefore, the area of the quadrilateral with the given vertices A(-8,6), B(-5,8), C(-2,6), D(-5,0) is 24 square units.