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Similar polygons have the same shape, but not necessarily the same size. Are rectangles with dimensions 8 x 5 and 25 x 40 similar?

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When the side-length of a square increases steadily, the perimeter and area increase as well.

If the side length increases in the sequence: 1, 2, 3, 4... then the perimeter increases in the sequence: 4, 8, 12, 16... and area, measured in unit-squares, increases in the sequence: 1, 4, 9, \(\fbox{?}\)

What number continues this pattern & is the area of a square with perimeter 16?

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When the side-lengths of a trapezoid increases steadily and proportionally, the perimeter and area increase as well.

If the side length of the top edge increases in the sequence: 1, 2, 3, 4... then the perimeter increases in the sequence: 5, 10, 15, 20... and area, measured in unit-trapezoids, increases in the sequence: 1, 4, 9, \(\fbox{?}\)

What number continues this pattern & is the area of a trapezoid (measured in unit-trapezoid) with perimeter 20?

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