Revised Coordinated Polygons I

This is easy to work out with the shoelace formula . We get

$A=\frac{[(-4) \times (-3) + 1 \times 5 + 3 \times 3 + (-2) \times (-1)]-[1 \times (-1) + 3 \times (-3) + (-2) \times 5 + (-4) \times 3]}{2}=\frac{28-(-32)}{2}=\frac{60}{2}=\boxed{30}$

Calculate the area of the two triangles using the cross product formula:

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import math

x1 = -4.0
y1 = -1.0

x2 = 1.0
y2 = -3.0

x3 = 3.0
y3 = 5.0

x4 = -2.0
y4 = 3.0

A = 0.0

#######################

v1x = x4 - x1
v1y = y4 - y1

v2x = x2 - x1
v2y = y2 - y1

cross = v1x*v2y - v1y*v2x

A = A + 0.5*math.fabs(cross)

#######################

v1x = x4 - x3
v1y = y4 - y3

v2x = x2 - x3
v2y = y2 - y3

cross = v1x*v2y - v1y*v2x

A = A + 0.5*math.fabs(cross)

#######################

print A

Wolfram/Alpha: area of polygon with vertices at {-4,-1},{1,-3},{3,5},{-2,3}, the answer is 30