Perimeter Formula

The perimeter of a geometric shape is the distance of its boundary. In other words, we can also define it as the total sum of the length of all the sides of the two-dimensional shape. Thus, the sum of the length of each side is the perimeter of any figure. Here, we shall discuss the perimeter formula for various geometric shapes. Let’s start learning!

Perimeter Formula

The Perimeter of the Square Formula

A square is a two-dimensional figure that has all the sides equal. SO now let us look at the perimeter formula of a square,

The perimeter of a square = 4a

Where ‘a’ is the length of a side of a square

The Perimeter of the Triangle Formula

A triangle is a 2D figure with three sides. An equilateral triangle has all three sides equal whereas an isosceles triangle has its two sides equal. A scalene has all three different-length sides.

The conditions essential for a triangle to exist are:

• • a + b > c
  • b + c > a
  • c + a > b

Perimeter of a Triangle = a + b + c

Where ‘a’ ‘b’ and ‘c’ are the sides of the triangle

The Perimeter of Rectangle Formula

A rectangle is a two-dimensional figure that has the opposite sides equal. 

Perimeter of a rectangle = 2(l + b)

Where ‘l’ is the length of a rectangle and ‘b’ is the breadth of the rectangle

The Perimeter of Parallelogram Formula

A parallelogram is a two-dimensional figure which has opposite sides equal and parallel to each other.

Perimeter of a Parallelogram = 2(B + H)

Where ‘B’ is the base and ‘H’ is the height of the said parallelogram

The Perimeter of a Trapezoid Formula

A trapezoid is a type of polygon. It is a quadrilateral that has at least a pair of sides parallel to each other. The altitude of a trapezium is the perpendicular distance between the parallel sides.

Perimeter of a trapezoid = a + b + c + d

Where a, b, c, d are Length of each of the sides of the trapezium

The Perimeter of a Kite Formula

A kite is a plane figure that has two pairs of equal size.

Perimeter of a kite = 2a + 2b

Where ‘a’ is the length of the first pair and ‘b’ is the length is the second pair

The Perimeter of a Rhombus Formula

A Rhombus is a plane figure with four same sides and four angles. These angles need necessarily be of 90 degrees. However, the opposite sides of the Rhombus need to be parallel to each other. The shape of a rhombus is often similar to the diamond shape. A square can also be called Rhombus as it satisfies all the conditions of a rhombus. The altitude of a rhombus is the distance at right angles to two sides. Also, it is to be noted here that the diagonals bisect each other at 90 degrees.

The perimeter of a rhombus = 4 × a

Where ‘a’ is the side of a rhombus

The Perimeter of a Hexagon Formula:

A hexagon is a polygon and has six sides and six edges. All six sides of a hexagon are equal and each internal angle is 120 degrees.

The perimeter of Hexagon = 6 × a

Where ‘a’ is the side of a hexagon

Solved Examples

Q.1. Find the perimeter of a parallelogram with base 6 cm and height 10 cm?

Solution:

Perimeter of a Parallelogram = 2 (B + H)
= 2 (6 + 10)
= 2 ˣ 16 cm
= 32 cm

Q.2. Find the perimeter of a triangle with sides 6 cm, 5 cm and 4 cm.

Solution:

Perimeter of a Triangle = a + b + c
= 6 + 5 + 4
= 15 cm

Q.3. Find the perimeter of a rectangle with length 10 cm and breadth  15 cm and 10 cm.

Solution:

The perimeter of a rectangle = 2 (length + breadth)

= 2 (10 + 15) cm

= 2 x 25 cm

= 50 cm