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.
Hints
- Triangle FBC has a right angle at B. We know FB = 5 cm and BC = 6 cm, so the area comes out directly.
- 5 × 6 ÷ 2 = 15 cm². But careful — that is triangle FBC before folding. Let us see what folding does.
- 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.
- The marked sides are the ones that land on each other: FB = FE and BC = EC. Folding preserves every length and every angle.
- 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
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?