Middle school · TypeLab 2D
Four-Arc Star (Invalsi)
Four-Arc Star (Invalsi): a composite plane figure made of a square with side 6.8 cm, minus a circle of radius 3.4 cm, minus a circle of radius 3.4 cm, minus a circle of radius 3.4 cm, minus a circle of radius 3.4 cm. It is a classic middle school geometry problem (“Cutouts & Benchmarks”). The net area is 9.95 cm² and the total perimeter is 21.36 cm.
Certified measurements (1:1 scale)
- Net area
- 9.95 cm²
- Total perimeter
- 21.36 cm
- Bounding box
- 6.8 × 6.8 cm
- Basic shapes
- 5
Step-by-step decomposition
- 1.Basesquare with side 6.8 cm46.24 cm²
- 2.−circle of radius 3.4 cm36.32 cm²
- 3.−circle of radius 3.4 cm36.32 cm²
- 4.−circle of radius 3.4 cm36.32 cm²
- 5.−circle of radius 3.4 cm36.32 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = l² − π·(l/2)² = r²·(4 − π)
The parts overlap or intersect, so the net area (9.95 cm²) comes from the exact Boolean operation rather than from a plain sum of the part areas.
Editable in PowerPoint & Office
The .PPTX file contains native DrawingML shapes: outlines, dimensions and labels stay separate objects you can recolor and edit in PowerPoint, Keynote and Google Slides. The .SVG file is pure vector art at 1:1 scale on an A4 sheet, ready for print, LaTeX and textbook layout.
