High school (grades 11–12) · TypeLab 2D
Asymmetric Biconvex Lens
Asymmetric Biconvex Lens: a composite plane figure made of a circle of radius 5.2 cm, intersected with a circle of radius 3.8 cm. It is a classic high school (grades 11–12) geometry problem (“Lenses & Reuleaux”). The net area is 19.09 cm² and the total perimeter is 16.87 cm.
Certified measurements (1:1 scale)
- Net area
- 19.09 cm²
- Total perimeter
- 16.87 cm
- Bounding box
- 3.8 × 7.07 cm
- Basic shapes
- 2
Step-by-step decomposition
- 1.Basecircle of radius 5.2 cm84.95 cm²
- 2.∩circle of radius 3.8 cm45.36 cm²
Area of each basic shape before the Boolean composition.
How to find the area
Area formula: A = R₁²·arccos(...) + R₂²·arccos(...) − ½√Δ
The parts overlap or intersect, so the net area (19.09 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.
