High school (grades 9–10) · TypeLab 2D
Octagon with Square Cutout
Octagon with Square Cutout: a composite plane figure made of a regular octagon with side 3.2 cm, minus a square with side 3.2 cm. It is a classic high school (grades 9–10) geometry problem (“Euclid & Polygons”). The net area is 39.2 cm² and the total perimeter is 38.4 cm, including 12.8 cm along the inner hole.
Certified measurements (1:1 scale)
- Net area
- 39.2 cm²
- Total perimeter
- 38.4 cm
- Outer boundary
- 25.6 cm
- Hole boundaries
- 12.8 cm
- Bounding box
- 7.73 × 7.73 cm
- Basic shapes
- 2
Step-by-step decomposition
- 1.Baseregular octagon with side 3.2 cm49.44 cm²
- 2.−square with side 3.2 cm10.24 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = 2(1+√2)·l² − l² = (1+2√2)·l²
Split the figure into basic shapes, find each area, add the joined parts and subtract the cut-outs: A = 49.44 − 10.24 = 39.2 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.
