Math

Irregular Polygon Area Calculator

Find the area of a polygon from up to five vertex coordinates (shoelace formula).

x₁

y₁

x₂

y₂

x₃

y₃

x₄

y₄

x₅ (optional)

y₅ (optional)

Calculated Output

Area 12

Formula: Shoelace: A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|

Step-by-Step Breakdown

1. Values used:

2. x₁ = 0

3. y₁ = 0

4. x₂ = 4

5. y₂ = 0

6. x₃ = 4

7. y₃ = 3

8. x₄ = 0

9. y₄ = 3

10. x₅ (optional) = 0

11. y₅ (optional) = 0

12.

13. Area = 12

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The math behind it

List the vertices in order; cross-multiply consecutive coordinates and sum, then halve the absolute value. Leave the 5th vertex at (0, 0) for a quadrilateral.

Worked Example

A 4×3 rectangle's vertices give area 12.

Frequently Asked Questions

Does vertex order matter?

List them in order around the polygon (clockwise or counter-clockwise); the absolute value handles the direction.

The math behind it

Worked Example

Frequently Asked Questions

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