What is a Perimeter?
A perimeter is the length of a line forming a closed shape. The perimeter of a triangle is the total distance of the three sides of a triangle, but this can be calculated using different pieces of information, depending on what you know.
A triangle is a 3- sided shape. When these sides meet on the inside, they form angles. Angles are measured in degrees.
There are three methods to calculate the perimeter of a triangle, depending on the information you have. Take a triangle, with sides of length a, b and c.
You could know some of the sides or angles and wish to calculate the full perimeter. Depending on the information you have, you calculate the perimeter using any one of the following methods with our Perimeter of a Triangle Calculator.
Method 1: You know the lengths of all sides
The formula for the perimeter of a triangle is a + b + c if you have the length of three sides. Adding these together gives you the perimeter.
P = a + b + c
Method 2: Side-Angle-Side
The second method for calculating the perimeter of a triangle can be used when you have the length for two sides as well as the angle between those sides.
When this angle, between the 2 known sides is 90°, this is an easy calculation to make using the Pythagorean Theorem. We call the side opposite the right angle, which is the longest side the hypotenuse. The law states that the square of the hypotenuse is equal to the sum of the square of the 2 shorter sides.
a2 + b2 = c2
Remember, this will only work where you are dealing with a right-angled triangle. From this, we can calculate the length of the 3rd side, and then add up the sides as before. This is easier because a right angle triangle is a simplified case.
However, when the triangle has no right angles, this becomes somewhat more complicated. In order to make this calculation, we use the law of cosines, or the cosine rule.
In this case, we will add the length of the three sides to find the perimeter, but need to calculate the length of the unknown side using the law of cosines. We use this as the angles are measured in degrees, using geometry and trigonometry to solve for the missing lengths.
The length of the unknown side is calculated using the following formula:
c2 = a2 = b2 – 2ab COS (c)
We can throw this into our equation for the perimeter to get:
P = a + b + √(a² + b² - 2 * a * b * cos(γ))
Where γ is the value of the angle we know.
Method 3: Angle-Side-Angle
For the 3rd method, we solve to get the length of the 2 unknown sides using the law of sines or the sin rule.
If we know the length of side a, and tow angles, γ and β,
P = a + (a / sin (β + γ)) * (sin (β) + sin(γ))
Our Perimeter of a Triangle Calculator will calculate this for you, just set what you know and enter those values.
The laws of sin and cosine work in this case because the angles of the triangle can be written as special relationships between the lines as diameters of a circle. These are just simplifications of proofs around inscribed angles within a circle and its diameters!
Real Life Applications:
You want to know how far you jogged around the corner block, or to fence your triangular vegetable garden. You can easily apply this formula to find the total distance around a triangle. In that case, you’re finding the perimeter!