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Analytic Geometry2D

Introduction to Analytic Geometry - Theory & Concepts - Analytic Geometry Polygon Area

Coordinate systems, distance formula, midpoint formula, slope, angle between lines, symmetry, and area of polygons.

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Polygon Area Explorer (Shoelace Formula)

Vertices

Vertex P1(1, 2)
X-Coord
Y-Coord
Vertex P2(3, 5)
X-Coord
Y-Coord
Vertex P3(4, 0)
X-Coord
Y-Coord
Calculated Area
6.5 sq units
Grid displaying polygon with verticesGrid line patternGrid area backgroundX AxisY AxisPolygon with area 6.5Vertex P1 at (1, 2)P1Vertex P2 at (3, 5)P2Vertex P3 at (4, 0)P3
Shoelace Formula Calculation:
A=12∣∑i=1n(xiyi+1−xi+1yi)∣A = \frac{1}{2} \left| \sum_{i=1}^n (x_i y_{i+1} - x_{i+1} y_i) \right|
A=12∣[(1⋅5)+(3⋅0)+(4⋅2)]−[(2⋅3)+(5⋅4)+(0⋅1)]∣A = \frac{1}{2} \left| [(1 \cdot 5) + (3 \cdot 0) + (4 \cdot 2)] - [(2 \cdot 3) + (5 \cdot 4) + (0 \cdot 1)] \right|A=12∣13−26∣=12∣−13∣=6.5A = \frac{1}{2} \left| 13 - 26 \right| = \frac{1}{2} \left| -13 \right| = 6.5

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