A square on every side
Draw a triangle with sides 3, 4 and 5. Build a square outwards on each side.
Step 1 of 4
- A 3, 4, 5 triangle.
- A square on the side of 3 holds 3 × 3 = 9 tiles.
- A square on the side of 4 holds 4 × 4 = 16 tiles.
- A square on the side of 5 holds 5 × 5 = 25 tiles.
Rule: a square on side s holds s × s unit tiles. A unit tile is a square of side 1. A square of side 3 has 3 rows of 3 tiles. The tile count is the square's area. To square a number is to multiply it by itself.
A right-angled triangle has one square corner, which is 90°. Squares can be built on any triangle's sides, not just right-angled ones. A triangle with sides 4, 5 and 6 has no square corner. Its three sides still have squares of 16, 25 and 36 tiles.
Drag the slider. Count the tiles inside.
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