Calculating the perimeter of a regular triangle: formula and illustrative exercises

The perimeter of a triangle is the total length of the sides of the triangle, whether it's equilateral, isosceles, or scalene. To understand how to calculate the perimeter of a regular triangle, let's delve into the detailed content below.

Methods to calculate the perimeter of a regular triangle

1. Formula for calculating the perimeter of a regular triangle

- The perimeter of a triangle is calculated using the following formula:

P = a + b + c

Where:
- P is the perimeter of the triangle
- a, b, c are the respective sides of the triangle

- Stating verbally: To find the perimeter of a triangle, add the lengths of its three sides together.

2. Some problems to find the perimeter of a regular triangle

Problem type 1: Finding the perimeter of a triangle given the lengths of its 3 sides

* Solution : We just need to apply the formula for calculating the perimeter of a triangle, substitute the values, and carefully compute to find the perimeter.

Problem type 2: Given the lengths of 2 sides and 1 angle formed by those sides

* Solution:

Step 1: Find the length of the remaining side by applying the Cosine Law

Triangle ABC has the lengths of its sides as follows: AB, AC, BC:

We have: - Calculating AB: AB² = BC² + AC² - 2.BC.AC.cosC
=> AB = √(BC² + AC² - 2.BC.AC.cosC)

- Calculating AC: AC² = AB² + BC² - 2.AB.BC.cosB
=> AC = √(AB² + BC² - 2.AB.BC.cosB)

- Calculating BC: BC² = AB² + AC² - 2.AB.AC.cosA
=> BC = √(AB² + AC² - 2.AB.AC.cosA)

 Interesting Reading

- How to calculate the perimeter of a right triangle
- How to calculate the perimeter of an isosceles triangle
- How to calculate the perimeter of an equilateral triangle

Step 2: Substitute the known quantities into the formula for calculating the perimeter of the triangle to find the result.

* Application Exercise: Triangle ABC has AB = 7 cm, BC = 6 cm, angle ABC = 60 degrees. Calculate the perimeter of triangle ABC.

Solution: According to the Cosine Law, we have:

AC = √(AB² + BC² - 2.AB.BC.cosB)
=> AC = √(72 + 62 - 2.7.6.cos60)
=> AC = √(72 + 62 - 2.7.6.0.5)
=> AC = √43 = 6.5 (cm)
The perimeter of triangle ABC is: 7 + 6 + 6.5 = 19.5 (cm)

Type 3: Given the radius of the inscribed circle and the area of the triangle, find the perimeter of the regular triangle

* Method:

Step 1: Calculate the semi-perimeter of the triangle

We calculate the semi-perimeter of the triangle using the formula for the area of the circumcircle of the triangle: S = p.r => p = S : r

Where:
- S represents the area of the triangle
- p represents the semi-perimeter of the triangle
- r represents the radius of the inscribed circle

Step 2: Calculate the perimeter of the triangle

Applying the formula: P = p x 2 (P is the perimeter of the triangle)

* Application Exercise: Triangle ABC circumscribes a circle with r = 4 cm and S_triangle = 30 cm². Calculate the perimeter of the regular triangle.

Solution:
- The semi-perimeter of the triangle is: 30 : 4 = 7.5 (cm)
- The perimeter of the triangle is: 7.5 x 2 = 15 (cm)
Answer: 15 cm.

In the above article, we have guided you on how to calculate the perimeter of a regular triangle and summarized some problem types for finding the perimeter when given related quantities. Besides calculating the perimeter of a regular triangle, you can also refer to formulas for calculating the perimeter of a right triangle, isosceles triangle, equilateral triangle, all of which are special triangles shared in Mytour's articles.

 Note

- Reinforce your knowledge and effective practice by solving 5th-grade triangle problems such as exercises on area, exercises on triangle perimeter.

- Before solving problems, you should review the formulas to apply them correctly. 

Refer to more ways to calculate the area of a triangle to easily solve related problems when encountering them. Types of problems calculating the perimeter of a triangle, calculating the area of a triangle are the most common problems in the Math curriculum, you need to grasp them firmly to avoid confusion when encountering them.