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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?

Two similar polygons have areas in the ratio of \( 16 : 25 \). What is the ratio of their perimeters?

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In this sequence of growing trapezoids, each trapezoid is constructed out of some number of smaller, similar "unit trapezoids." The first figure in the sequence is a single unit trapezoid, the next figure contains 4, the next is made of 9...

What is the perimeter of a trapezoid made out of 100 unit-trapezoids?

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In this sequence of similar, growing "V" figures, each V is constructed out of some number of identical small, square tiles.

What is the **perimeter** of the next, similar V-figure in this sequence, which would be made out of 48 square tiles?

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If the yellow, green, red, and black trapezoids in this figure are all similar, and if the yellow trapezoid has area 64, what is the area of the entire figure (yellow + green + red + black)?

Hint: Can you use the ratio of scale between the yellow and green trapezoids to calculate the area of the green trapezoid quickly?...

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