High school (grades 9–10) · TypeLab 2D
Hollow Regular Pentagon
Hollow Regular Pentagon: a composite plane figure made of a regular pentagon with side 5.2 cm, minus a regular pentagon with side 2.4 cm. It is a classic high school (grades 9–10) geometry problem (“Euclid & Polygons”). The net area is 36.61 cm² and the total perimeter is 38 cm, including 12 cm along the inner hole.
Certified measurements (1:1 scale)
- Net area
- 36.61 cm²
- Total perimeter
- 38 cm
- Outer boundary
- 26 cm
- Hole boundaries
- 12 cm
- Bounding box
- 8.41 × 8 cm
- Basic shapes
- 2
Step-by-step decomposition
- 1.Baseregular pentagon with side 5.2 cm46.52 cm²
- 2.−regular pentagon with side 2.4 cm9.91 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = 1.7205·(L² − l²)
Split the figure into basic shapes, find each area, add the joined parts and subtract the cut-outs: A = 46.52 − 9.91 = 36.61 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.
