Two overlapping squares of different length, find the area of shaded region

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Two overlapping squares of different length, find the area of shaded region
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Комментарии
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Connect E and C, which makes two triangles, both of heights 3/2, and bases 1 and 2.
Area = ½*3/2 *(1+2)=9/4

harikatragadda
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Rotate the right angle FEH by 90°, 180°, 270° respectively. Then you have 4 regions, each with the same area as the shaded area. Together they fill they square ABCD, which has area 3·3 = 9. Hence the area is 9/4.

Bruno_Haible
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Another possibility:
Extend the sides of the big square till they intersect the sides of the small square, thus making four Quadrilaterals. Since these extended lines are orthogonal, they make the same angles at the sides of the small square, and thus the four quadrilaterals are Similar. But the diagonals of the Quadrilaterals are also equal, hence they are also Congruent. Therefore Area of each quadrilateral = ¼(Area of the small square)= 9/4

harikatragadda