KEVOS® MAKEOS · Geometry
Plane Figure Area and Perimeter
What area and perimeter does this flat shape have?
Area, perimeter and equivalent circle and square of common plane figures: circle, ring, sector, ring sector, rectangle, parallelogram, trapezoid, fillet (spandrel), parabolic segment and cycloid.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Shape | choice | The figure; the option text says which dimension each input means. |
| Dimension A | mm | Main dimension as described for the shape. |
| Dimension B | mm | Second dimension where the shape needs it. |
| Dimension C (height) | mm | Height where the shape needs it. |
| Angle (sectors) | ° | Included angle of a sector or ring sector. |
Method and formulas
- Circle πd²/4; ring π(D² − d²)/4; sector πr²θ/360; ring sector π(R² − r²)θ/360; rectangle AB; parallelogram base × height; trapezoid (a + b)h/2.
- Fillet (spandrel) between a quarter circle and its tangents: r²(1 − π/4) = 0.2146 r².
- Parabolic segment 2/3 × chord × height; cycloid 3πr² with arc length 8r.
- Equal-area circle diameter = √(4A/π); equal-area square side = √A.
- Example: a trapezoid with parallel sides 100 and 60 mm and height 40 mm has an area of 3,200 mm².
Limitations
- Ideal geometric figures; fillets and corner radii on real parts change the area.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find plate, gasket and section areas
- Estimate material for cut shapes
- Check areas on drawings
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Area
- Perimeter (where defined)
- Diameter of a circle and side of a square with the same area
Interpreting the result
- Use the polygon area tool for irregular shapes defined by corner coordinates.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 66–81. Topic reference; no source tables or recommended settings are reproduced.
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