If the area of a square and rectangle are equal. The side of square is 12 cm and length of the rectangle is 16 cm, then what would be the perimeter of rectangle?

A teacher has a rope with length equal to L cm. Using the entire rope, he forms the edges of a non-square rectangle with area equal to A cm2. What is the length of the smaller side of this rectangle, in cm ? (In terms of L and A)

In rectangle ABCD, a semicircle CPS is drawn as shown below.
The semicircle’s diameter is shared with and extends beyond side BC, it intersects side AB at Q, and it is tangent to side AD at S.
If CQ = 10, what is the area of rectangle ABCD?

In the following figure, everything is square other then large rectangle. If the green square has side length 1 and the brown square has side length 2 then what is the area of the rectangle?

Semicircle AB is flipped upside down and translated horizontally so the new semicircle CD is tangent to AB, as shown. The line through AB is tangent to the semicircle CD and the line through CD is tangent to the semicircle AB.

If each semicircle has a diameter equal to 2, what is the length of AD?
Express your answer in the form √x + √y for positive integers x < y.