Total area of the blue and red triangles?
A hard-level "Area" problem.Put P anywhere inside and the two opposite triangles always sum to half. A problem that makes you want to drag P around and check.
GivenParallelogram ABCD has area 60 cm². P is a point inside it, but its position is not given
Hints
- The clue is that the answer is fixed even though P's position is not. Look at the two bases: AB and DC are opposite sides of a parallelogram, so they are parallel and equal in length.
- Now the heights. Call the distance from P down to AB "ア", and from P up to DC "イ". Move P up or down and each of them changes.
- But ア and イ added together are exactly the parallelogram's own height, because AB and DC are parallel. Wherever P goes, that total never changes.
- Adding the two areas gives AB × ア ÷ 2 + AB × イ ÷ 2 = AB × (ア + イ) ÷ 2 — that is, "base × the parallelogram's height ÷ 2".
- "Base × height" is the parallelogram's area itself, and we divide it by 2 — so the answer is exactly half the parallelogram: 60 ÷ 2
Answer 30cm²
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?