Formulate a theorem on the diameter of a perpendicular chord and its converse.

If the given quadrangle is a rectangle with sides of 10 and 12 cm, then its area can be found as the product of length and width.

In the form of a formula, this can be written as:

S = a * b.

We just have to substitute the values into the formula and make calculations:

S = 10 * 12 = 120 cm ^ 2.

If the given quadrangle turns out to be a rhombus, then to calculate its area we will use the formula:

S = a * b * sin a.

In addition to the lengths of the sides, we also need to know the angle between them.

We can write down the answer.

Answer: 120 cm ^ 2 is the area of a rectangle.