the vertices of a quadrilateral are A(-4,-3), B(2,-3), C(4,-6) and D(-2,-6)
Find the area of quadrilateral ABCD
draw it. It's a parallelogram with base=6, height = 3
So, area = bh = 18
To find the area of quadrilateral ABCD, you can use the shoelace formula. The shoelace formula, also known as the Gauss's area formula, calculates the area of a polygon given the coordinates of its vertices.
Here are the steps to find the area using the shoelace formula:
1. Write down the coordinates of the given vertices: A(-4, -3), B(2, -3), C(4, -6), and D(-2, -6).
2. Create two lists, X and Y, to separate the x-coordinates and y-coordinates of the vertices, respectively. Write down the x-coordinates of the vertices in the X list and the y-coordinates in the Y list.
X: -4, 2, 4, -2
Y: -3, -3, -6, -6
3. Multiply each x-coordinate in the X list with the y-coordinate immediately below it in the Y list. Write down these products in another list, called P.
P: (-4) * (-3), (2) * (-3), (4) * (-6), (-2) * (-6)
= 12, -6, -24, 12
4. Multiply each y-coordinate in the Y list with the x-coordinate immediately below it in the X list. Write down these products in another list, called Q.
Q: (-3) * 2, (-3) * 4, (-6) * (-2), (-6) * (-4)
= -6, -12, 12, 24
5. Add up all the values in the P list and subtract the sum of the values in the Q list. This will give you the area of the quadrilateral.
Area = (12 + (-6) + (-24) + 12) - (-6 + (-12) + 12 + 24)
= 0 - 30
= -30
The area of quadrilateral ABCD is -30 square units. Notice that the area is negative, indicating that the vertices might not have been ordered in a counterclockwise direction.