High school (grades 9–10) · TypeLab 2D
Scalloped Hexagonal Gear
Scalloped Hexagonal Gear: a composite plane figure made of a regular hexagon with side 4.2 cm, minus a circle of radius 1 cm, minus a circle of radius 1 cm, minus a circle of radius 1 cm, minus a circle of radius 1 cm, minus a circle of radius 1 cm, minus a circle of radius 1 cm, minus a circle of radius 1.2 cm. It is a classic high school (grades 9–10) geometry problem (“Euclid & Polygons”). The net area is 35.03 cm² and the total perimeter is 33.3 cm, including 7.54 cm along the inner hole.
Certified measurements (1:1 scale)
- Net area
- 35.03 cm²
- Total perimeter
- 33.3 cm
- Outer boundary
- 25.76 cm
- Hole boundaries
- 7.54 cm
- Bounding box
- 7.4 × 7.27 cm
- Basic shapes
- 8
Step-by-step decomposition
- 1.Baseregular hexagon with side 4.2 cm45.83 cm²
- 2.−circle of radius 1 cm3.14 cm²
- 3.−circle of radius 1 cm3.14 cm²
- 4.−circle of radius 1 cm3.14 cm²
- 5.−circle of radius 1 cm3.14 cm²
- 6.−circle of radius 1 cm3.14 cm²
- 7.−circle of radius 1 cm3.14 cm²
- 8.−circle of radius 1.2 cm4.52 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = (3√3/2)·l² − 2·π·r_v² − π·r₀²
The parts overlap or intersect, so the net area (35.03 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.
