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Area Perimeter of Triangle

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Last updated date: 24th Jul 2024
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Introduction

A triangle's perimeter is calculated as the whole length of its border. A triangle is a polygon with three sides that may be classed depending on the length of its sides and angles. Depending on the type of triangle, there are several formulae and techniques for calculating the perimeter.


What is the Triangle's Perimeter?

The perimeter of a triangle is calculated by the sum of its three sides. The term perimeter is derived from two Greek words: "peri" (circumference) and "metron" (measure). The perimeter of any 2D form is defined as the entire distance around it. Because the perimeter represents the length of a shape's boundaries, it is stated in linear units.


Real-Life Triangle Perimeter Example: Assume we need to fence the triangle park. To get the measurements of the fence, sum the lengths of the park's three sides. The perimeter of a triangle is the length or distance of the triangle's border.


Area of the triangle

Several formulae may be used to determine the area of a triangle. The area of the triangle can be calculated by the Herons formula or through the trigonometric formula. However, the basic method for calculating the area of a triangle is:

$\frac{1}{2}\times \text{base} \times \text{height}$


Triangle Perimeter Formula

To find the perimeter of a triangle, just sum the lengths of the given sides. The simplest formula for calculating a triangle's perimeter is:

Perimeter = a + b+ c

Let us examine this formula using several sorts of triangles.


Scalene Triangle Perimeter

A scalene triangle has three sides that are of different lengths. The perimeter of a scalene triangle may be computed by adding the uneven sides together. The perimeter of a scalene triangle is calculated as Perimeter = a + b+ c, where "a", "b", and "c" are the three separate sides.


Isosceles Triangle Perimeter

An isosceles triangle has two sides that have the same length. The perimeter of an isosceles triangle may be computed by adding the equal and unequal sides together. The perimeter of an isosceles triangle is given by:

Perimeter = 2a + b units, where “a” is the equal-length side and “b”, denotes the third side.


Equilateral Triangle Perimeter

All of three sides of an equilateral triangle are of equal length. The perimeter of an equilateral triangle is calculated as follows:

Perimeter of an equilateral triangle = (3a) units, where “a” is the length of each side of the triangle.


Right Triangle Perimeter

A right-angled triangle or right triangle is a triangle in which one of the angles is 900. By adding the provided sides, the perimeter of a right triangle may be computed. The perimeter of a right triangle can be calculated by the formula:

Perimeter = a + b+ c units, is right triangle perimeter.


Isosceles Right Triangle Perimeter

An isosceles right triangle is a right triangle having two equal sides and two equal angles. By adding the supplied sides, the perimeter of an isosceles right triangle may be computed.


P = 2l + h is the formula for calculating the perimeter of an isosceles right triangle, where l is the length of the triangle's two equal legs or sides and h is the hypotenuse.


How to Calculate the Perimeter of a Triangle?

The perimeter of a triangle may be computed using the following steps:

Step 1: Write down the dimensions of all the triangle's sides and double-check that they all have the same unit.

Step 2: Add the sums of all the sides.

Step 3: Provide the solution together with the unit.


Sample questions

1. Equilateral triangle is the triangle with

a. Two different side length

b. All sides with the same length

c. Two sides of the same length

d. No equal sides

Ans: All sides with the same length


2. Right angle triangle has

a. One angle as right angle

b. Two angles at right angle

c. All the angles at right angle

d. All the sides having the same length

Ans: One angle as a right angle


3. To apply a fence around a triangular park we need to calculate

a. Area of triangle

b. Length of side of the triangle

c. Perimeter of the triangle

d. Angle of the triangle

Ans: Perimeter of the triangle

FAQs on Area Perimeter of Triangle

1. Find the length of the isosceles triangle if sides of equal length are of 17 units and the perimeter of the triangle is 48 units. 

Perimeter of the triangle = 48 units 

An isosceles triangle has two sides equal in length = 17 units 

Perimeter = 2a + b

48 =2 x 17 + b

48 = 34 + b

b = 14

So, the length of a missing side is 14 units. 

2. A book shaped in an equilateral triangle has a length of a side 12 inches. Find the perimeter of the triangle. 

Side of the triangle (a)= 12 inches 

Perimeter = 3a 

Perimeter = 3 x 12 

= 36inches 

3. The length of the base of a right-angled triangle is 4 units and the hypotenuse is 5 units. Find the perimeter of the triangle.

To find the third side we will apply Pythagoras theorem:

a2 + b2 = c2

Where a = 4 and c = 5

42 +b2 = 52 

16+b2 = 25 

b2 =25 -16 

b2 = 9 

b = 3 

As, a = 4 b = 3, and c = 5

So, the perimeter of the triangle = a + b + c

P = 4 + 3 +5

P = 12 units

4. The perimeter of the equilateral triangle is 279 units. Find the length of the side of the equilateral triangle. 

Perimeter = 279 units
Perimeter = 3a

279 = 3 x a

$\frac {279}{3} = a$

93 = a

5. A triangle with sides of 20, 35, and 60 units needs to be fenced. What type of triangle is it and also find its perimeter. 

The triangle has three sides with different lengths. So, it is a scalene triangle.

perimeter = a + b + c

P = 20 + 35 + 60

P = 115 units