High school (grades 11–12) · TypeLab 2D
Asymmetric Arbelos of Archimedes
Asymmetric Arbelos of Archimedes: a composite plane figure made of a semicircle of radius 4.5 cm, minus a semicircle of radius 3 cm, minus a semicircle of radius 1.5 cm. It is a classic high school (grades 11–12) geometry problem (“Archimedes & Hippocrates”). The net area is 14.13 cm² and the total perimeter is 27.68 cm.
Certified measurements (1:1 scale)
- Net area
- 14.13 cm²
- Total perimeter
- 27.68 cm
- Bounding box
- 8.99 × 4.5 cm
- Basic shapes
- 3
Step-by-step decomposition
- 1.Basesemicircle of radius 4.5 cm31.81 cm²
- 2.−semicircle of radius 3 cm14.14 cm²
- 3.−semicircle of radius 1.5 cm3.53 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = π·r₁·r₂ = ¼·π·CD²
Split the figure into basic shapes, find each area, add the joined parts and subtract the cut-outs: A = 31.81 − 14.14 − 3.53 = 14.13 cm².
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.
