High school (grades 11–12) · TypeLab 2D
Twin Lunes of Hippocrates
Twin Lunes of Hippocrates: a composite plane figure made of a triangle with base 4.8 cm and height 3.6 cm, joined with a semicircle of radius 2.4 cm, joined with a semicircle of radius 1.8 cm, minus a semicircle of radius 3 cm. It is a classic high school (grades 11–12) geometry problem (“Archimedes & Hippocrates”). The net area is 8.64 cm² and the total perimeter is 22.62 cm.
Certified measurements (1:1 scale)
- Net area
- 8.64 cm²
- Total perimeter
- 22.62 cm
- Bounding box
- 6.6 × 6 cm
- Basic shapes
- 4
Step-by-step decomposition
- 1.Basetriangle with base 4.8 cm and height 3.6 cm8.64 cm²
- 2.+semicircle of radius 2.4 cm9.05 cm²
- 3.+semicircle of radius 1.8 cm5.09 cm²
- 4.−semicircle of radius 3 cm14.14 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A(L₁) + A(L₂) = ½·a·b
Split the figure into basic shapes, find each area, add the joined parts and subtract the cut-outs: A = 8.64 + 9.05 + 5.09 − 14.14 = 8.64 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.
