The length that is the height
A tile-layer fixes floor tiles. This one measured along the slanted edge. Was that the height?
- A rectangle: side and height both 5.
- Lean it: height stays 5, the slant becomes 6.
- 8 × 5 = 40 — right.
- 8 × 6 = 48 — wrong.
Only one length is the height
No. A square corner is a right angle. The height is measured square across, not along the slant.
The height goes from the base to the far corner, square across. It equals a side only when the corner is square. Usually the shape leans, and the slanted side is longer.
Any side can be the base. Measure the height to that base, from the opposite corner.
The height can fall outside the shape. Points are written as (across, up). A triangle has its base from (0, 0) to (6, 0). Its top corner is at (12, 8). Draw a line straight down from that corner. It meets the line of the base at (12, 0). That is beyond the base. The height is 8. The area is ½ × 6 × 8 = 24.
The base is drawn thick. Tap the height.
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