Solve aligned triangle overlap using dimensions, scaling, and area percentages. Compare small and large shapes. Download clean reports for study, modeling, and validation tasks.
| Small Base | Small Height | Scale Factor | Large Base | Large Height | Overlap % | Small Area | Large Area | Overlap Area |
|---|---|---|---|---|---|---|---|---|
| 6 | 4 | 1.5 | 9 | 6 | 40 | 12 | 27 | 4.8 |
| 8 | 5 | 2 | 16 | 10 | 25 | 20 | 80 | 5 |
| 10 | 7 | 1.2 | 12 | 8.4 | 60 | 35 | 50.4 | 21 |
Similarity ratio: k = Large Base ÷ Small Base = Large Height ÷ Small Height
Large dimensions: Large Base = Small Base × k, Large Height = Small Height × k
Triangle area: Area = 0.5 × Base × Height
Area ratio: Large Area ÷ Small Area = k²
Overlap area: Overlap Area = Small Area × (Overlap Percent ÷ 100)
Overlap similarity scale: Overlap Scale = √(Overlap Percent ÷ 100)
Overlap dimensions: Overlap Base = Small Base × Overlap Scale, Overlap Height = Small Height × Overlap Scale
Union area: Union Area = Small Area + Large Area − Overlap Area
Overlapping similar triangles appear in geometry, computer vision, and model preprocessing. A smaller triangle may represent a source pattern. A larger one may represent a scaled target pattern. This calculator helps you compare them quickly. It measures dimensions, area ratios, and shared coverage in one place.
In AI and machine learning, geometric scaling is common. Image regions are resized during detection, segmentation, and feature extraction. Similar triangle logic also appears in projection, alignment, and shape normalization. This calculator supports fast inspection of scale changes. It also helps when a shared region must be estimated before training or validation.
The tool starts with a smaller triangle base and height. You can then provide a scale factor, a larger base, or a larger height. The calculator derives the missing dimensions using triangle similarity. It computes the small area, large area, and area ratio. It also estimates overlap using a percentage of the smaller triangle area.
This calculator uses an aligned overlap model. That means both triangles keep the same orientation and shape. The overlap input represents the shared part of the smaller triangle area. From that value, the tool estimates overlap area and an equivalent overlap triangle size. This gives a practical planning model for analysis and documentation.
The results section is designed for quick review. You can see the large triangle dimensions, overlap share, visible areas, and total union area. These values are useful for educational work, synthetic data design, annotation checks, and scaling experiments. The export options also make record keeping easier. You can save results as CSV or PDF for later use.
Use consistent units for every input. Enter accurate dimensions. Then choose a sensible overlap percentage. The calculator will return a clean report immediately. This keeps geometry checks fast and repeatable. It is a practical helper for both learning and applied technical work.
It calculates dimensions, scale ratio, areas, overlap area, and union area for two aligned similar triangles. It is useful when one triangle is a scaled version of another.
It means the shared region is measured as a percentage of the smaller triangle area. This keeps the model simple and consistent for planning, study, and reporting.
Yes. You can enter a scale factor, a large base, or a large height. The calculator derives the missing matching values from triangle similarity rules.
The calculator shows an error. Similar triangles must keep the same scale ratio across matching sides. If the ratios differ, the inputs are inconsistent.
Geometric scaling is common in image analysis, object detection, annotation design, and feature alignment. Similar triangle reasoning helps explain some of those spatial relationships.
No. This version assumes aligned, similarly oriented triangles. It does not compute rotated polygon intersections or arbitrary geometric clipping between complex shapes.
Yes. Use the same unit for every length input. If base and height use different units, the calculated areas and overlap values will not be reliable.
Yes. After calculation, use the CSV button for spreadsheet-friendly data or the PDF button for a clean printable report.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.