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What is the area of the folded-over triangle?

A hard-level "Area" problem.Folding changes none of the area, the lengths or the angles. Find which pre-fold piece it matches and you only ever calculate once.

GivenA rectangle of paper 16 cm by 6 cm. Corner B is folded over along the line joining C (top right) to F on the bottom edge, where FB = 5 cm.

Area ★★★★☆☆ What is the area of the folded-over triangle? 16cm 6cm 5cm AB FC

Hints

  1. Triangle FBC has a right angle at B. We know FB = 5 cm and BC = 6 cm, so the area comes out directly.
  2. 5 × 6 ÷ 2 = 15 cm². But careful — that is triangle FBC before folding. Let us see what folding does.
  3. Folding copies the shape exactly across the crease. So the blue triangle after folding has precisely the same area as the red one before it.
  4. The marked sides are the ones that land on each other: FB = FE and BC = EC. Folding preserves every length and every angle.
  5. So the answer is the number we already had: 15 cm². In folding problems, fix "the area does not change" first and you avoid a long detour.

Answer 15cm²

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