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November Question of the Month for Geometry

Find the area of the convex polygon in the plane with vertices at the points whose coordinates are (-3,3), (2,3), (5,1), (1,-7), and (-5,-3).

Solution:

The area of the red square is 10*10=100

The area of region I is 6*2/2=6

The area of region II is 3*2/2=3

The area of region III is 8*4/2=16

The area of region IV is 4*6/2=12

The total area is 100-(6+3+16+12)=63
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