The perimeter of the Triangle: The perimeter of any two-dimensional figure depends on the area around it. Any closed shape's perimeter can be calculated by adding the lengths of its sides. In this tutorial, you will first learn what the perimeter is and how to calculate it for different kinds of triangles with known side lengths. You'll be able to view the subject from more angles thanks to the solved instances. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty. Our online school aims to help students prepare for Board Exams by ensuring that students have conceptual clarity in all the subjects and can score their maximum in the exams.
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What is the Perimeter of a Triangle?
The sum of the lengths of the sides is the perimeter of any polygon.
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In the case of a triangle-Perimeter = Sum of the three sides
Always include units in the final answer.
If the sides of the triangle are measured in centimeters, then the final answer should also be in centimeters.
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Perimeter of Triangle Formula
The formula for the perimeter of a closed-shaped figure is usually equal to the length of the outer line of the figure. Therefore, in the case of a triangle, the perimeter will be the sum of all three sides. If a triangle has three sides a, b, and c, then,
Perimeter = a + b + c
Where "a" is the length of one side of the triangle, "b" is the length of another side, and "c" is the length of the third side.
For example, if the lengths of the sides of a triangle are 4, 5, and 6, the perimeter would be:
Perimeter = 4 + 5 + 6 = 15
So the perimeter of the triangle is 15.
Note that the perimeter of a triangle is a measure of the distance around the outside of the triangle, not the area inside the triangle.
To find the area of a triangle, you can use a different formula, such as the formula for the area of a triangle using base and height, or the formula for the area of a triangle using the lengths of all three sides (also known as Heron's formula).
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Perimeter of an Isosceles, Equilateral and Scalene Triangle
Where a, b, c, and l denote the side lengths and P denotes the perimeter.
To find the perimeter of a triangle, add the lengths of all three of its sides together. If A, B, and C side measurements and X is the perimeter, then A+B+C= X
Perimeter of Right Triangle
A right triangle has a base(b), hypotenuse(h), and perpendicular(p) as its sides, By the Pythagoras theorem, we know,
h square = b square + p square
Therefore, the Perimeter of a right angle triangle= b + p + h
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Examples
Let us consider some examples of the perimeter of a triangle:
Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm, and 2 cm.
Solution: Let,
a = 5 cm
b = 4 cm
c = 2 cm
Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11
Therefore, the answer is 11 cm.
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Example 2: Find the perimeter of a triangle whose each side is 10 cm.
Solution: Since all three sides are equal in length, the triangle is equilateral.
i.e. a = b = c = 10 cm
Perimeter = a + b + c
= 10 + 10 + 10
= 30
Perimeter = 30 cm.
Example 3: What is the missing side length of a triangle whose perimeter is 40 cm and two sides are 10 cm each?
Solution: Given,
Perimeter = 40 cm
The length of the two sides is the same i.e. 10 cm.
Thus, the triangle is isosceles.
Using formula: P = 2l + b
40 = 2 * 10 + b
40 = 20 + b
or b = 20
The missing side length is 20 cm.
What does the Perimeter of a Triangle Mean?
How to Calculate the Perimeter of a Triangle?
Calculate the Perimeter of a Right Triangle with Base as 3 cm and height as 4 cm.
First, using the Pythagorean theorem, calculate the hypotenuse of the right triangle.
h =√(base2+perpendicular2)
h = √(32+42)
h = √(9 + 16)
h = √25
Or, h = 5 cm
So, the perimeter of the triangle = 3 + 4 + 5 = 12 cm.
