Find the area of a polygon with the given vertices? A(1, 4), B(-2, -2) C(-7, -2), D(-4, 4) Please show work.
Consider that the polygon ABCD is composed of the triangle ABC and ACD.
To find the area of a triangle whose vertices coordinates are given we can use the Cramer's Rule, described in:
Finding the area of a triangle using the determinant of a matrix
Evaluating the determinant of the Cramer's Rule we get:
Repeating the points
If we plot those points we'll see that A and D are in the same line (
Beyond that, since A and D are in the same line and also B and C are in the same line
Two segments of line of the same size in lines parallel to each other, yet the segments are not aligned: it means that the polygon is a parallelogram, whose equation of area is
The separation or distance between the two lines (
So the area of the polygon ABCD, a parallelogram, is