It is known that the circumference of rectangle ABCD is 18, e and F are the points on the edges AB and BC respectively, and AE = BF = 1. If EF is perpendicular to BD, the area of this rectangle can be calculated

Let AB = x, BC = y, perimeter = 2x + 2Y = 18, that is, x = 9-y; triangle EBF and triangle BCD are similar triangles, so be / BF = BC / CD; be = ab-ae = Y-1, BF = 1, BC = x, CD = y, so Y-1 = x / y, substituting x = 9-y can get y = 3, (- 3 discarded); so x = 9-3 = 6, rectangular area is 3 * 6 = 18

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1. As shown in the figure, ▱ ABCD, if EF crosses the intersection of diagonal lines o, ab = 4, ad = 3, of = 1.3, then the perimeter of quadrilateral BCEF is______ ．
2. In the parallelogram ABCD, if EF passes through the intersection of diagonals o, ab = 4, ad = 3, the perimeter of quadrilateral BCEF = 9.6, the length of of of can be obtained
3. If AB = 5, BC = 7, OE = 2, then the perimeter of EFDC is () A.14 B.15 C.16 D.18
4. If the parallelogram ABCD and EF cross the focus o, ab = 3, BC = 5 and OE = 2 of the diagonal, what is the perimeter of the parallelogram ADFE
5. Given that the side length of square ABCD is 2 and point P is a point on diagonal AC, the maximum value of (. AP +. BD) ·(. Pb +. PD) is______
6. If the side length of square ABCD is 1 and point P moves on line AC, then the value range of AP & nbsp; · & nbsp; (Pb + PD) is______ ．
7. In known trapezoidal ABCD, ad is parallel to BC, angle ABC = 60 degrees, ab = AD + BC = 4, M is the midpoint, find the size of 1 angle dam, the length of AM and BM
8. As shown in the following figure: in trapezoidal ABCD, the area of triangle AEC is 4, the area of triangle CED is 6, and the area of triangle bed is 9? In the picture, the two diagonals are pulled up and divided into four triangles. There are two diagonals A and C (from left to right) at the top and two diagonals B and D at the bottom. The intersection of the diagonals is e
9. P is a point inside the square ABCD and a point e outside the square ABCD. Find the degree of angle BPE P is a point inside the square ABCD, and there is a point e outside the square ABCD, satisfying the angle Abe = angle CBP, be = BP, and finding the degree of angle BPE
10. As shown in the figure, e is an edge point in the square ABCD. If the triangle Abe is an equilateral triangle, find the degree of the angle BCE
11. As shown in the figure, in rectangle ABCD, AE = BF = 3, EF ⊥ ed intersects BC at point F, and the circumference of rectangle is 22. Calculate the length of EF
12. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) Verification: AC ‖ de; (2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, and explain the reason
13. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) verification: AC ‖ de（ 2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, please explain the reason (do not judge parallelogram)
14. The quadrilateral ABCD is a rectangle,
15. ABCD is a rectangle ∠ EDC = ∠ cab ∠ Dec = 90 ° (1) verification: AC ‖ de (2) through B as BF ⊥ AC connected to f to judge the shape of becf and explain the reason
16. 1. As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) prove: AC ‖ de; (2) make BF ⊥ AC at point F through point B, connect
17. As shown in the figure, in square ABCD, the diagonal lines AC and BD intersect at point O, and the points EF are on AC and BD respectively, and BF = CE connects be, AF.AF There is a relation between be and quantity
18. As shown in the figure, the diagonal lines AC and BD of rectangular ABCD intersect at point O, EF ⊥ BD at point O, ad at point E, BC at point F, and EF = BF
19. Parallelogram ABCD parallelogram abef is on the same side AB, m, n are on the diagonal AC, BF respectively, and am: AC = FN: FB to prove Mn / / plane ADF
20. ABCD and abef are parallelograms, m and N are the points on diagonal AC and BF respectively, and am: FN = AC: BF