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Semi Perimeter

In geometry, we might have come across different types of formulas such as perimeter, area, height, volume, etc. Semi perimeter is one of the most commonly used measurements when dealing with polygons. It is the measurement related to plane figures, i.e. two-dimensional shapes. Semi perimeter can be calculated for different plane figures using simple formulas. In this article, you will learn the definition of semi perimeter and the formula of semi perimeter for different shapes, along with examples.

Learn: Perimeter

What is Semi Perimeter?

As we know, the perimeter is the distance around the shape, whereas the semi perimeter is half its perimeter. For any given polygon, the semi perimeter can be calculated by dividing its circumference by 2. Although it has a simplistic derivation from the perimeter, the semi perimeter frequently appears in formulas related to triangles and other shapes to give it a separate name. If the semi perimeter is part of a formula, it is represented by the letter “s”.

Semi Perimeter Formula

From the definition of semi perimeter, we can write the formula as:

Semi perimeter = Perimeter/2

However, semi perimeter formulas for various shapes and polygons are tabulated below:

Shape

Formula

Explanation

Semi Perimeter of a Triangle formulas

Semi perimeter of Equilateral triangle

3a/2

a = Length of the side of an equilateral triangle

Semi perimeter of Isosceles triangle

a + (b/2)

a = Length of congruent sides

b = Length of the third side

Semi perimeter of Right angle triangle

(base + height + hypotenuse)/2

Height = Perpendicular

Hypotenuse = The longest side

Semi perimeter of Scalene triangle

(a + b + c)/2

a, b, c are the measures of lengths of three sides

Semi Perimeter of Curved Shapes Formulas

Semi Perimeter of Circle

(2πr)/2 or πr

r = Radius of circle

Semi perimeter of Semicircle

(πr + 2r)/2

r = Radius of the semicircle

Semi Perimeter of Quadrilaterals Formulas

Semi Perimeter of Rectangle Formula

2(l + b)/2 or l + b

l = Length

b = Breadth

Semi Perimeter of Square

(4a/2) or 2a

a = Side of a square

Semi perimeter of any quadrilateral

(a + b + c + d)/2

a, b, c, d are the length of sides of the quadrilateral

Also, check: What is the length?

Applications of Semi Perimeter

The formula of semi perimeter can be applied in many geometry formulas. Let’s have a look at one of the important formulas related to triangles where we apply semi perimeter.

Heron’s formula = √[s(s – a)(s – b)(s – c)]

This formula is used to find the area of a scalene triangle.

Here,

s = Semi perimeter = (a + b + c)/2

a, b and c are the lengths of sides.

Similarly, we can calculate the area of a cyclic quadrilateral using semi perimeter as:

Area = √[(s – a)(s – b)(s – c)(s – d)]

This is the simplest form of Brahmagupta’s formula.

Here,

Semi perimeter = s = (a + b + c + d)/2

Solved Examples

Example 1:

Find the semi perimeter of a triangle whose sides are 14 cm, 8 cm and 11 cm.

Solution:

Let the measure of slides of a triangle be:

a = 14 cm

b = 8 cm

c = 11 cm

Semi perimeter = s = (a + b + c)/2

= (14 + 8 + 11)/2

= 33/2

= 16.5

Therefore, the semi perimeter of a given triangle is 16.5 cm.

Example 2:

What is the semi perimeter of a square whose side measure 15 cm?

Solution:

Given,

Side of a square = a = 15 cm

Semi perimeter = 2a = 2 × 15 = 30 cm

Alternatively,

Perimeter of a square = 4a = 4 × 15 = 60 cm

Semi perimeter of square = Perimeter/2 = 60/2 = 30 cm

Frequently Asked Questions on Semi Perimeter

What is the semi perimeter formula?

Semi perimeter is the half of perimeter for any shape. That means, by dividing the perimeter of a given figure by 2, we get the semi perimeter.
Thus, the formula of semi perimeter is:
Semi perimeter = Perimeter/2

How do you denote the semi perimeter?

The letter “s” is used to denote the semi perimeter of a given shape in geometry.

What is the formula of the semi perimeter of a rectangle?

The formula for the semi perimeter of a rectangle is given by:
Semi perimeter of rectangle = 2(l + b)/2 = (l + b)
That means the semi perimeter of a rectangle is equal to the sum of the measures of length and breadth.

What is the correct form of semi perimeter in Heron’s formula?

The correct form of semi perimeter in Heron’s formula is: s = (a + b + c)/2

What is the semi perimeter of the isosceles triangle?

The formula for finding the semi perimeter of an isosceles triangle is:
s = a + (b/2)

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