# 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.

##### 2 Answers

#### Explanation:

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:

For

A(1, 4)

B(-2, -2)

C(-7, -2)

For

A(1, 4)

C(-7, -2)

D(-4, 4)

S=30

#### Explanation:

Repeating the points

A(1,4)

B(-2,-2)

C(-7,-2)

D(-4,4)

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