area of an irregular polygon

Geometry Level 2

Given the coordinates of the vertices, find the area of the green polygon shown.


The answer is 40.

A Former Brilliant Member by A Former Brilliant Member

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3 solutions

Frederick Rose
Sep 3, 2018

I USED ACAD

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auto cad is the easiest way. i am also expert in auto cad

A Former Brilliant Member - 2 years, 9 months ago
Edwin Gray
Jun 27, 2018

Connect (-1,1) to (-4,-4) and (-4,-4) to (5,4), creating 3 triangles. Compute all distances between vertices by the distance formula, then apply Herron's formula to each of the 3 triangles, getting 15.5, 10.5, and 14, whose sum is 40. Ed Gray

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Using the shoelace formula we get an area of 40 40 .

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