Area of a Triangle

1. 1Cut Along the MiddleJoin the midpoints of the two sides, then cut the top off along that line and straight down its middle. The cuts sweep in one after the other; two small pieces are now ready to move.Cut: middle line + middle of the top
2. 2Flip the Two Top PiecesRotate each top piece half a turn around the midpoint of its side — first the left one, then the right. The triangle rearranges itself into a new shape — without stretching or losing a single piece.Same pieces, new shape
3. 3The Height, HalvedThe altitude comes back as a ghost line and splits in two: 6 = 3 + 3. The rectangle reaches only to the split — its height is 3 cm, exactly half of the triangle’s height.6 ÷ 2 = 3 cm
4. 4The Rectangle's AreaThe numbers climb off the diagram into the computation: 8 × 3 = 24 cm². Cutting and flipping never changed the amount of surface, so the triangle's area is 24 cm² too.8 × 3 = 24 cm²
5. 5The FormulaThe rectangle's height was the triangle's height halved, so the area of a triangle is (base × height) ÷ 2 = (8 × 6) ÷ 2 = 24 cm². The opening question is answered: only half.S = (a × h) ÷ 2
6. 6Check by DoublingDouble the rectangle and the empty top half of the frame fills back in: 24 × 2 = 48 = 8 × 6 — exactly the whole frame, so 24 cm² is right.24 × 2 = 48 ✓
7. 7Half of Its FrameThree questions to check yourself: (1) Double the base, keep the height — the area doubles too, to 48 cm². (2) Halve the height — the area halves as well. (3) A completely different-looking triangle with the same base 8 cm and the same height 6 cm — its area is still 24 cm², because area is the surface covered, not the shape.S = (a × h) ÷ 2

Change the numbers to test the engine with any sum & difference problem: