The perimeter P of a square is given by P = 4 * side. If P = 32 cm, then side = 32/4 = 8 cm.

A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right triangle.

The area of a circle is given by A = πr². If the radius is doubled (r becomes 2r), the new area is A' = π(2r)² = 4πr², which is four times the original area.

In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.

In a 30-60-90 triangle, the sides opposite the 30 degrees and 60 degrees angles are in the ratio 1:√3.

The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².

The length of the diagonal d of a rectangle can be found using the Pythagorean theorem: d = √(length² + width²) = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.

The perimeter of a rectangle is given by P = 2(length + width). Here, P = 2(10 + 5) = 30 cm.