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 sides have right angles. It is a special type of parallelogram with equal angles. A rectangle with four equivalent sides is known as a square. Now let us learn the properties of a rectangle in this article.

Properties of Rectangle

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 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 \(\sqrt{a^{2}+b^{2}}\)
  • 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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