High school (grades 11–12) · TypeLab 2D
Pointed Gothic Window
Pointed Gothic Window: a composite plane figure made of a circle of radius 5.6 cm, intersected with a circle of radius 5.6 cm, minus a rectangle 8 × 6.4 cm, joined with a rectangle 5.6 × 4.2 cm. It is a classic high school (grades 11–12) geometry problem (“Lenses & Reuleaux”). The net area is 42.76 cm² and the total perimeter is 25.73 cm.
Certified measurements (1:1 scale)
- Net area
- 42.76 cm²
- Total perimeter
- 25.73 cm
- Bounding box
- 5.6 × 9.05 cm
- Basic shapes
- 4
Step-by-step decomposition
- 1.Basecircle of radius 5.6 cm98.52 cm²
- 2.∩circle of radius 5.6 cm98.52 cm²
- 3.−rectangle 8 × 6.4 cm51.2 cm²
- 4.+rectangle 5.6 × 4.2 cm23.52 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = b·h + b²·(π/3 − √3/4)
The parts overlap or intersect, so the net area (42.76 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.
