# Properties of 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: $d = \sqrt{a^{2}+b^{2}}$
• 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

### Example

Question:

Find the perimeter of a rectangle whose sides are 10cm and 5cm, respectively.

Solution:

Given:

a = 10 cm

b = 5 cm

According to the properties of a rectangle, the perimeter of a rectangle is:

Perimeter, P = 2a +2b units

P = 2 (a+b) units

Now, substitute the values

P = 2(10+5)

P = 2(15)

P = 30 cm

Therefore, the perimeter of a rectangle is 30 cm.

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