How much larger is イ than ア?
A hard-level "Area" problem.When a problem asks for a difference, you may add or subtract the same thing from both sides — which lets you delete an awkward shared region without ever computing it.
GivenA 10 cm square with an arc of radius 10 cm centred at A, and the diagonal BD / π = 3.14
Hints
- Both ア and イ are bounded by a mix of curve and straight lines, and neither yields to a direct calculation. Notice that we are only asked for the difference.
- ア and イ sit side by side with a shared region between them — where triangle BCD and sector ABD overlap.
- Add the shared region to ア and you get exactly triangle BCD — and a triangle's area we can find.
- Add the same region to イ and you get sector ABD — also easy to find.
- Adding the same thing to both leaves the difference unchanged. Triangle BCD = 10 × 10 ÷ 2 = 50 cm², sector ABD = 10 × 10 × 3.14 ÷ 4 = 78.5 cm². 78.5 − 50
Answer 28.5cm²
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?