Perimeter of Triangles Formula: Definition, Types, Solved Examples
Perimeter of Triangles Formula: the perimeter of any shape with sides is just the total length around it. Think about a triangle, which has three sides. To find its perimeter (we call it "P"), you just add up the lengths of those three sides.
Manoj Kumar14 Sept, 2023
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Perimeter of Triangles Formula: The concept of perimeter is fundamental when dealing with two-dimensional geometric shapes. It represents the total distance around a closed figure. Calculating the perimeter of such shapes involves adding up the lengths of all their sides. We will explore the idea of perimeter. We will pay special attention to figuring out how to find the perimeter of different kinds of triangles when we already know the lengths of all their sides. Plus, we will include some example problems to make it easier for you to understand this topic.
Defining the Perimeter of a Triangle
In geometry, when we talk about the perimeter of any shape with sides, we mean adding up how long all those sides are. For a triangle, which is a three-sided shape, the perimeter (which we call "P") is just the sum of the lengths of its three sides: Perimeter = Sum of the three sides Including units in your final answer is crucial for accuracy. If the sides of the triangle are measured in centimeters, make sure to express the perimeter in centimeters as well.Also Check - Sets Formula
Perimeter Formula for Triangles
To find the perimeter of a closed shape, you typically add up the lengths of its outer edges. For triangles, this means summing the lengths of all three sides. If a triangle has three sides labeled as "a," "b," and "c," then the formula for its perimeter (P) is as follows: Perimeter, P = a + b + cAlso Check - Data Handling Formula
Perimeter of Different Types of Triangles
Let's explore how to calculate the perimeter of various types of triangles, such as equilateral, isosceles, and scalene triangles: Equilateral Triangle: For an equilateral triangle, where all three sides have the same length (l), calculating the perimeter is straightforward. You can use the following formula:
Perimeter (P) = 3l
Isosceles Triangle:
In an isosceles triangle, where two sides are the same length and the third side is represented as "b," you can determine the perimeter using the following formula:
Perimeter (P) = 2a + b
Also Check - Ratio and Proportion Formula
Scalene Triangle: In a scalene triangle, where all three sides have different lengths (a, b, and c), you would apply the same basic formula mentioned earlier to calculate the perimeter:
Perimeter (P) = a + b + c
Perimeter of a Right Triangle
A right triangle has three sides: base (b), hypotenuse (h), and perpendicular (p). According to the Pythagoras theorem, these sides are related as follows:
c 2 = a 2 +b 2
Therefore, the perimeter (P) of a right triangle can be calculated as: Perimeter = b + p + hAlso Check - Polynomials Formula
Solved Examples
Example 1: Determine the perimeter of a shape with side lengths of 6 cm, 3 cm, and 4 cm. Solution: Here is what we know: Side "a" = 6 cm Side "b" = 3 cm Side "c" = 4 cm To get the perimeter, we add up all these side lengths: Perimeter (P) = a + b + c = 6 cm + 3 cm + 4 cm = 13 cm So, the perimeter is 13 cm. Example 2: Determine the perimeter of a triangle with all sides measuring 10 cm. Solution: Because all three sides have the same length, this triangle can be classified as an equilateral triangle. Side "a" = 10 cm Side "b" = 10 cm Side "c" = 10 cm To calculate the perimeter, simply use the formula for an equilateral triangle: Perimeter (P) = 3l = 3 * 10 cm = 30 cm Hence, the perimeter is 30 cm. Example 3: Find the missing side length of a triangle with a perimeter of 40 cm and two sides measuring 10 cm each. Solution: Given: We know that the perimeter (P) of the triangle is 40 cm. Two sides (l) are each 10 cm in length, making it an isosceles triangle. To find the missing side (b), we can use the formula for an isosceles triangle: Perimeter (P) = 2l + b Substitute the known values: 40 cm = 2 * 10 cm + b Simplify: 40 cm = 20 cm + b Now, to find "b," we subtract 20 cm from both sides: b = 40 cm - 20 cm = 20 cm So, the missing side length is 20 cm.Perimeter of Triangles Formula FAQs
What is the perimeter of a triangle?
The perimeter of a triangle is the total distance around the triangle, obtained by summing the lengths of all its sides.
How do I calculate the perimeter of a triangle?
To find the perimeter of a triangle, simply add up the lengths of all three of its sides.
Are units important when expressing the perimeter of a triangle?
Yes, it's crucial to include units (e.g., centimeters, inches) in the final answer to indicate the measurement scale.
What formula do we use to find the perimeter of a triangle?
The formula for the perimeter (P) of a triangle with sides "a," "b," and "c" is: P = a + b + c.
How do I calculate the perimeter of an equilateral triangle?
For an equilateral triangle with side length "l," the perimeter is given by: P = 3l.
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