jugoslav

Too late; the correct answer is right above your post. 

By using the real numbers, we can simplify this simple question (and answer) even more.

Let a side of the square be 2 units

(I'll use hecticar's diagram)

1/    ∠a ≅ ∠c = arctan(DQ / AD) ≈ 26.565º

2/    ∠b = 90º - (∠a + ∠c) ≈ 36.87º

3/     sin(∠b) = 0.6    or   3/5 

Let SV be  x

x (x + 3) = 3 * 18

x² + 3x - 54 = 0       (solve with the quadratic formula)

x = 6

SW = 9

This polygon has 24 sides.

Let the area of the square XSWZ be 529 u².          side = √529

Area of the square QEZA = 529 - 273 = 256 u²      side = √256

Yellow area     A = [23(23-16)] /2 + [16(23-16)] /2  

The sine of angle PAQ is 0.6

ST * SU = SV * SW           solve for SV using quadratic formula

Instead of perpendicular, read vertical. 

Something's missing here!!!

The sum of those two (given) angles is 180º, but that does not necessarily mean that the perpendicular lines are parallel!!!

6)    L : W = 5 : 3          L : 45 = 5 : 3           L = (5 * 45) / 3          L = 75

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7)           C = 10

T : C = 6 : 5              T : 10 = 6 : 5           T = (10 * 6) / 5       T = 12

P : T = 8 : 3               P : 12 = 8 : 3           P = (12 * 8) / 3         P = 32