As shown in the figure, △ ABC's edge AB = 3, AC = 2, I, II, III respectively represent the square with AB, AC, BC as the edge. What is the maximum value of the sum of the areas of the three shadow parts in the figure?

Rotate △ CFH clockwise 90 ° around point C to make CF coincide with BC, and H rotate to the position of H ', ∵ quadrilateral achm is a square, ∠ ACh = 90 °, CA = ch = ch ′, ∵ a, C, H' are on a straight line, BC is the middle line of △ ABH ', ∵ s △ CHF = s △ BCH' = s △ ABC, similarly: s △ BDG = s △ AEM = s △ ABC

RELATED INFORMATIONS

1. As shown in the figure, the area of △ ABC is ∠ BAC = 150 °, ab = 20cm, AC = 30cm?
2. The triangle ABC and AD are the middle line on the side of BC, the angle B is three times of angle a, and the angle CDB is 45 ° to prove that ABC is a right triangle
3. In △ ABC, D is the midpoint of AC, de ⊥ BC is e, be & sup2; - ce & sup2; = AB & sup2;, it is proved that ABC is a right triangle
4. In the right triangle ABC, CD is the middle line on the hypotenuse ab. given ∠ B = 30 ° and AC = 5cm, then AB and CD are equal to 3Q
5. In the right triangle ABC, ∠ C = 90 ° CD ⊥ AB in D, ∠ a = 60 ° CD = √ 3, AB is obtained
6. In a right triangle ABC, if AB = m and angle a = a, then the length of the high Cd on the hypotenuse ab
7. The circle with radius R is circumscribed to the isosceles right triangle ABC, and the inscribed circle radius of the triangle ABC is R. then the ratio of the circumference of the big circle to that of the small circle is? 1. If the circle with radius R is circumscribed to the isosceles right triangle ABC, and the inscribed circle radius of the triangle ABC is r, the ratio of the circumference of the big circle to that of the small circle is () 2. If the side view of a cone is a semicircle with radius a, the height of the cone is () It is known that the side expansion of two cones with equal generatrix can just form a circle, and the ratio of their side area is 1:2, then the ratio of their height is ()
8. If the two right angles of a right triangle are 3 and 4, then the radius r of its circumcircle=______ , inscribed circle radius r=______ ．
9. 6. In RT triangle ABC, angle c = 90 °, BC = 5, sin a = 0.7, find cos a, Tan a 8. The length of two adjacent sides of a parallelogram door panel is 62.31cm and 35.24cm respectively, and the included angle between them is 35.40 ° to calculate the area of this board. (results two decimal places are reserved.)
10. In RT △ ABC, if Tan α = 2, then sin α =?, cos α =? There is no picture
11. [online, etc] in △ ABC, ab = 7, BC: AC = 4:3, find the value range of triangle ABC perimeter
12. As shown in the figure, in △ ABC, ad ⊥ BC, be ⊥ AC, the perpendicular feet are D and e respectively. AD and be intersect at point F. if BF = AC, find the size of ∠ ABC
13. As shown in the figure, △ ABC, the angle ABC = 45, ad is perpendicular to point D, be is perpendicular to point E, ad and be intersect at point h, if AC = 10, then BH=
14. As shown in the figure: in △ ABC, ad ⊥ BC is in D, be ⊥ AC is in E, ad and be intersect in H and BH = AC, find the degree of ∠ HCD
15. In the triangle ABC, the angle ABC is 45 degrees. H is the intersection point of high AD and be. BH = AC, BH is perpendicular to AC
16. Ad and be are the heights of the triangle ABC. The two heights intersect at a point h. If BH and AC are equal in length, the angle BCH =? Degree
17. Under the following conditions, it is impossible to determine the congruence of △ ABC and △ def_ A.∠B=∠E=90°,AB=DE,AC=DF B.∠B=∠E=90°,∠A=∠D,AC=DF C.∠B=∠E=90°,∠C=∠F,AB=EF D.∠B=∠E=90°,AB=DE,BC=EF
18. In the following conditions, it can be judged that △ ABC and △ def are congruent () A. The girth of AB = De, BC = EF, BC = EF, a = DC, a = D, C = f, AC = EFD, ab = De, BC = EF, and the girth of △ ABC = the girth of △ def
19. Among the following conditions, () A. AB=DE，∠B=∠E，∠C=∠FB. AC=DF，AB=DE，∠C=∠DC. AB=EF，∠A=∠E，∠B=∠FD. ∠A=∠F，∠B=∠E，AC=DF
20. As shown in the figure, two congruent triangles ABC and def are overlapped. Fix the triangle ABC and do the following operation for the triangle def The triangle def moves to the right along the line AB (that is, point d moves in the line AB). When point d moves to the midpoint of AB, what is the shape of the quadrilateral cdbf? Explain the reason