## Table of contents:

- 1. How to find the perimeter of a triangle, knowing the three sides
- 2. How to find the perimeter of a triangle, knowing its area and the radius of the inscribed circle
- 3. How to calculate the perimeter of a triangle, knowing the two sides and the angle between them
- 4. How to find the perimeter of an equilateral triangle, knowing one side
- 5. How to calculate the perimeter of an isosceles triangle, knowing the side and base
- 6. How to find the perimeter of an isosceles triangle, knowing the side and height
- 7. How to calculate the perimeter of a right triangle, knowing the legs
- 8. How to find the perimeter of a right triangle, knowing the leg and hypotenuse

2023 **Author**: Malcolm Clapton | [email protected]. Last modified: 2023-05-22 06:26

Choose a formula based on known quantities.

## 1. How to find the perimeter of a triangle, knowing the three sides

Just count the sum of all sides.

- P is the required perimeter;
- a, b, c - sides of the triangle.

## 2. How to find the perimeter of a triangle, knowing its area and the radius of the inscribed circle

Multiply the area of the triangle by 2.

Divide the result by the radius of the inscribed circle.

- P is the required perimeter;
- S is the area of the triangle;
- r is the radius of the inscribed circle.

## 3. How to calculate the perimeter of a triangle, knowing the two sides and the angle between them

First, find the unknown side of the triangle using the cosine theorem:

- Multiply one side by the other, by the cosine of the angle between them, and by 2.
- Calculate the sum of the squares of the known sides and subtract from it the number obtained in the previous step.
- Find the root of the result.

Now add the two previously known sides to the found side.

- P is the required perimeter;
- b, c - known sides of the triangle;
- ɑ is the angle between the known sides;
- a - unknown side of the triangle.

## 4. How to find the perimeter of an equilateral triangle, knowing one side

Multiply the side by 3.

- P is the required perimeter;
- a - any side of the triangle (recall that in an equilateral triangle all sides are equal).

## 5. How to calculate the perimeter of an isosceles triangle, knowing the side and base

Multiply the side by 2.

Add base to the result.

- P is the required perimeter;
- a - the side of the triangle (in an isosceles triangle, the sides are equal);
- b - the base of the triangle (this is the side that differs in length from the rest).

## 6. How to find the perimeter of an isosceles triangle, knowing the side and height

Find the side and height squares.

Subtract the second from the first number.

Find the root of the result and multiply it by 2.

Add the two sides to the resulting number.

- P is the required perimeter;
- a - lateral side of the triangle;
- h is the height (the perpendicular dropped to the base of the triangle from the side of the opposite vertex; in an isosceles triangle, the height divides the base in half).

## 7. How to calculate the perimeter of a right triangle, knowing the legs

Find the squares of the legs and count their sum.

Extract the root of the resulting number.

Add both legs to the result.

- P is the required perimeter;
- a, b - legs of a triangle (sides that form a right angle).

## 8. How to find the perimeter of a right triangle, knowing the leg and hypotenuse

Count the squares of the hypotenuse and leg.

Subtract the second from the first number.

Find the root of the result.

Add leg and hypotenuse.

- P is the required perimeter;
- a - any leg of the rectangle;
- c - hypotenuse (the side that lies opposite the right angle).