The side length of the square ABCD is a. place a vertex of the square omnp large enough on the symmetric center O of the square ABCD The side length of square ABCD is a Operation and calculation: place a vertex of the square omnp large enough on the symmetric center O of the square ABCD, and OM ⊥ BC, Op ⊥ DC. Try to find the area of the quadrilateral OECF of the overlapping part of two squares Thinking and exploration: if the square omnp is rotated at any angle around point O, is be equal to CF? Why? Can we find the area of quadrilateral OECF? What do you find?

The side length of the square ABCD is a. place a vertex of the square omnp large enough on the symmetric center O of the square ABCD The side length of square ABCD is a Operation and calculation: place a vertex of the square omnp large enough on the symmetric center O of the square ABCD, and OM ⊥ BC, Op ⊥ DC. Try to find the area of the quadrilateral OECF of the overlapping part of two squares Thinking and exploration: if the square omnp is rotated at any angle around point O, is be equal to CF? Why? Can we find the area of quadrilateral OECF? What do you find?

(1) The overlap area is 1 / 4A & sup2;
(2) If the square omnp is rotated at any angle around point O, then be and CF are equal, and the area of quadrilateral OECF is 1 / 4A & sup2;
prove:
A quadrilateral ABCD is a square
∴OB⊥OC,OB=OC,∠OBE=∠OCF=45°
∵∠EOF=90°
∴∠APE=∠CPF
∴△BOE≌△COF
∴BE=CF
∵△BOE≌△COF
∴S△BOE=S△COF
S quadrilateral OECF = s △ OBC = 1 / 4A & sup2;
It is found that no matter how many degrees are rotated, the area of quadrilateral OECF remains unchanged, be = CF