# VectorPaint parallelogram dissections: fix base and perpendicular height before area

Language: en
Canonical: [VectorPaint parallelogram dissections: fix base and perpendicular height before area](<https://allluckly.cn/en/guides/vectorpaint-parallelogram-cut-shear-height/>)
中文：[中文 HTML](<https://allluckly.cn/guides/vectorpaint-parallelogram-cut-shear-height/>)
English: [English HTML](<https://allluckly.cn/en/guides/vectorpaint-parallelogram-cut-shear-height/>)
Published: 2026-11-10T00:00:00+08:00
Modified: 2026-11-10T09:39:21+08:00
Author: Bison

Translate a left triangle to fill the right gap,checking area24 while distinguishing slant side,perpendicular height and bounding box.

English translation of the [Chinese original](<https://allluckly.cn/guides/vectorpaint-parallelogram-cut-shear-height/>), translated on 2026-11-10. Original publication dates, attribution, code and version notes are retained.

Greater slant does not necessarily mean greater area. Fix base 6, perpendicular height 4, draw coordinates and translate one triangular piece into a rectangle. This checks dissection and equal-base/height conditions, distinct from equal-perimeter comparison, without automatic cutting, area measurement or animation.

## Record four corners and the coordinate convention

Use vertices(0, 0), (6, 0), (8, 4), (2, 4) under downward-increasing exercise y. Both horizontal bases are 6, separated perpendicularly by 4; slant displacement is(2, 4). Scale/translate uniformly without retaining units after nonuniform stretching. Preserve pale references and labels, explicitly restricting this example to offset 2 less than base 6. These are geometry units, not material dimensions, and coordinates remain externally traceable.

## Measure height perpendicular to the bases

Mark height 4 on a perpendicular to both bases. Slant length√20≈4.472 is not height, and 6×4.472 is not the area. The 8×4 bounding rectangle has area 32, also different. Label base, height, slant and bounds explicitly, with colour supplementary. An exterior height reference is acceptable with clear perpendicular direction and corresponding bases; not every oblique top-to-bottom line is a height. Stroke width does not enter ideal lengths.

## Cut the left triangle at x 2

Divide vertically from(2, 0) to(2, 4), isolating triangleA with vertices(0, 0), (2, 0), (2, 4), legs 2/4, area 4. Preserve the remainder and distinguish the cut from the outer boundary. Construct separate closed paths in a copy, checking gap-free assembly without assuming a knife/difference command. Hiding A should reveal a coherent remainder. A background-colour patch need not create an independently movable piece; identify the chosen method.

## Translate the triangle six units right

Add 6 to each x coordinate of A, producing(6, 0), (8, 0), (8, 4), with unchanged y, no rotation/scaling. It fills the upper-right gap and forms a rectangle spanningx 2–8, y 0–4, width 6, height 4. Check the same vector at all vertices before outline; dragging one point near the gap while deforming others is invalid. A remains area 4, remainder 20, total 24. Preserve before/after separately rather than counting both triangle copies.

## Compare a separate offset 3 with the same base and height

For a separate offset 3 use(0, 0), (6, 0), (9, 4), (3, 4), retaining base 6/height 4. Cut atx 3 and translate by 6 to a 6×4 rectangle spanning 3–9, area 24; the cut triangle now has area 6, not 4. These two shears share area under equal base/height, not arbitrary vertex changes. Offsets exceeding the base require a different dissection rather than unchanged application here. Preserve offset 2 and list changed versus fixed quantities.

## Keep geometric shear distinct from perspective scaling

Compare on one unit grid with equal bases/heights. Do not stretch one view to equal outer bounds and attribute the result to geometry. Slant, perimeter and bounds may change while area remains 24; label quantities rather than saying only “size”. Cut lines/arrows do not add area. Transparent before/after overlays need position labels so overlap does not imply extra material. Static comparisons are not claimed app animations.

## Inspect seams and scale statements in output

Save and inspect PNG positions, especially width 6 acrossx 2–8 rather than 8. For white seams inspect shared endpoints; for darker overlap inspect an unhidden original triangle before changing area labels. Hide unwanted manual grids/references actively. Individually scaled thumbnails require scale labels and cannot compare area visually. Preserve geometry records separately from output; apparent fit does not replace pointwise translation checks.

## Check height, piece and movement in order

For 32 inspect bounding-box use; for base times slant inspect height definition; for a skewed reconstruction inspect translation-only movement. Check scaling before compensating through remainder edits. Retain both offsets, coordinates, area pairs 4+20 and 6+18, and shared 24, traceable to graphics/calculations. This is a clear dissection, not automatic area verification, physical cutting design or a claim that every shape uses this same one-piece move.

## Related tutorials and sources

[VectorPaint equal-perimeter rectangles: check boundary length separately from area](<https://allluckly.cn/en/guides/vectorpaint-equal-perimeter-different-areas/>), [VectorPaint translation and reflection: check each vertex coordinate and orientation](<https://allluckly.cn/en/guides/vectorpaint-coordinate-translation-reflection/>).

Checked on November 10, 2026: VectorPaint public version 1.0.8, requiring iOS / iPadOS 17.0 or later. Capability scope follows the [official App Store listing](<https://apps.apple.com/cn/app/id1587272880>) and [Apple public version lookup](<https://itunes.apple.com/lookup?id=1587272880&country=cn>). This is an original exercise to perform independently; use controls in your installed version. Manual construction and external records do not imply new automatic analysis features. No step-by-step physical-device, private-file or all-output-environment testing is claimed.