Rectangle ‒ Description

A rectangle is a parallelogram in which all interior angles are 90 degrees, or right angles. The opposite sides of a rectangle are always equal in length. A square is a special case of a rectangle where all four sides are of equal length.

Each rectangle has two diagonals, which are line segments connecting opposite vertices. In this figure, the diagonals are line segments AC and BD, also denoted u₁ and u₂. These diagonals are always equal in length and longer than either side of the rectangle. Unlike in a square, the diagonals of a rectangle do not intersect at a right angle. Each diagonal divides the rectangle into two equal halves, and together they divide the rectangle into four quarters. The diagonals bisect each other. If the midpoint of the rectangle is marked as S (as shown), then the length of the segment AS is equal to the length of the segment CS.

The perimeter of a rectangle is the total length of all its sides, calculated as the sum of the lengths of all four sides: a + b + a + b. Since opposite sides are always equal in length, the perimeter can also be expressed as 2a + 2b.

The area of a rectangle is the amount of surface it covers. It is calculated by multiplying the length of one side by the length of the adjacent side, giving the area as a · b.



**Mathematical formulas**:



Perimeter:

P = 2a + 2b



Area:

A = ab



Diagonal:

u₁ = √(a² + b²)



Radius of the circumscribed circle:

rₒ = ½u₁