What is the total area of the three sectors?
A hard-level "Area" problem.When the parts cannot be found one by one, look only at the total. The angles stay unknown, but "they add to 180°" turns all three sectors into a single semicircle.
GivenAt each corner of a triangle, a sector of radius 4 cm is drawn / π = 3.14
Hints
- The three sectors have different angles. Call the triangle's angles ア, イ and ウ. Trying to work them out one at a time gets nowhere — we do not know any of them.
- But one thing is certain: the three angles of a triangle always total 180°. Each is unknown, yet their sum is not.
- A sector's area is "circle × angle ÷ 360". All three have the same radius, 4 cm, so the total is just circle × (ア+イ+ウ) ÷ 360.
- ア+イ+ウ is 180°, and 180 ÷ 360 is exactly one half. So the three sectors together make one semicircle of radius 4 cm — whatever shape the triangle has.
- So 4 × 4 × 3.14 ÷ 2 = 25.12 cm² — and we never found a single angle.
Answer 25.12cm²
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?
Browse by idea
- Add, then subtract — an overlap is a counting problem
- Circles and sectors — multiply by π once, at the very end