Rectangle

A rectangle is a two-dimensional plane figure with four sides. A rectangle is a four-sided polygon in which the opposite sides are parallel and equal to each other. It is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. The rectangle is a special type of parallelogram with all its angles equal. A rectangle with four equal sides is known as a square. Now let us learn the properties of rectangle in this article.

Rectangle Properties

The fundamental properties of rectangles are:

• A rectangle is a quadrilateral
• The opposite sides are parallel and equal to each other
• Each interior angle is equal to 90 degrees
• The sum of all the interior angles is equal to 360 degrees
• The diagonals bisect each other
• Both the diagonals have the same length
• A rectangle with side lengths a and b has the perimeter as 2a+2b units
• A rectangle with side lengths a and b has the area as: ab sin 90 = ab square units
• The sum of the interior angles is equal to 360 degrees
• A diagonal of a rectangle is a diameter of its circumcircle
• If a and b are the sides of a rectangle, then the length of each diagonal is: d=√a²+b²
• The diagonals bisect each other at different angles. One is acute, and another one is an obtuse angle
• If the two diagonals bisect each other at right angles, then the rectangle is known as a square
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the longer parallel sides. In this case, the height of the cylinder is equal to the width of a rectangle. Also, the cylinder diameter is equivalent to the length of a rectangle
• A cylinder is obtained when the rectangle is rotated along the line joining the midpoint of the shorter parallel sides. In this case, the height of the cylinder is equal to the length of a rectangle. Similarly, the cylinder diameter is equivalent to the width of a rectangle

Parallelogram

Properties of a parallelogra

• Opposite sides are parallel and congruent
• Opposite angles are congruent
• Adjacent angles are supplementary.
• Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.
• If one of the angles of a parallelogram is a right angle then all other angles are right and it becomes a rectangle.

Important formulas of parallelograms

• Area = L * H

• Perimeter = 2(L+B)

Squares

Properties of a square

• All sides and angles are congruent.
• Opposite sides are parallel to each other.
• The diagonals are congruent.
• The diagonals are perpendicular to and bisect each other.
• A square is a special type of parallelogram whose all angles and sides are equal.
• Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.

Important formulas for Squares

• If ‘L’ is the length of the side of a square then length of the diagonal = a √2.
• Area = a².
• Perimeter = 4a