Geometry Problem 1323: Discover the Fascinating World of Squares, Angle Trisectors, Diagonals, and Regular Dodecagons with 30-60 Degrees: Unveiling the Secrets of Area!

IIn a blue square A1A2A3A4 with side length 'a', the trisectors of angles A1, A2, A3, A4 and diagonals intersect at points B1, B2, B3, B4, C1, C2, C3, C4, D1, D2, D3, ..., D12 as shown in the figure. We need to prove the following statements: (1) B1B2B3B4 is a square (yellow); (2) D1D4D7D10 is a square (red); (3) C1C2C3C4 is a square (orange) ; (4) D1D2...D12 is a regular dodecagon (green); (5) Area of B1B2B3B4 = Formula to prove; (6) Area of B1B2B3B4 = 2 times the area of D1D4D7D10; (7) Area B1B2B3B4 = 3 times the area of C1C2C3C4; (8) Area D1D2...D12 = 3/4 times the area of B1B2B3B4.

Geometry Problem 1323: Square, Angle Trisector, Diagonal, Regular Dodecagon, Area

Square, angles flow,
Diagonals in tow,
Dodecagon's grace,
Area's captivating space,
30-60 degrees embrace!


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