Find the perimeter of a triangle with coordinates calculator

geometry

Table of Contents Show

How to Use the Perimeter of a Triangle Calculator?
What is Meant by the Perimeter of a Triangle?
Perimeter of a triangle formula
Rules for solving a triangle
Examples: find the perimeter of a triangle
How do you find the area of a triangle with coordinates?
How do you find the area of a triangle with 3 vertices?
How do you determine if a triangle is right with coordinates?

triangle

What I want to Find

Perimeter Area Area using Heron's Formula Height

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What is Given

Height

What is Given

Area

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triangle-area-perimeter-calculator

Value of side ‘a’ :

Value of side ‘b’ :

Value of side ‘c’ :

Perimeter of Triangle:

The Perimeter of a Triangle Calculator is a free online tool that displays the perimeter of a triangle when the side values are given. BYJU’S online perimeter of a triangle calculator tool performs the calculation faster, and it displays the perimeter of a triangle in a fraction of seconds.

How to Use the Perimeter of a Triangle Calculator?

The procedure to use the perimeter of a triangle calculator is as follows:

Step 1: Enter the side values of a triangle in the input field

Step 2: Now click the button “Calculate” to get the perimeter value

Step 3: Finally, the perimeter of a triangle will be displayed in the output field

What is Meant by the Perimeter of a Triangle?

In Geometry, a triangle is a closed two-dimensional figure with three sides, three vertices and three angles. Based on the number of sides and angles, the triangle can be classified into different types. The area of a triangle is the region occupied by the shape triangle. The perimeter of a triangle is the length of the complete boundary of a triangle. In other words, the perimeter of a triangle is the sum of all the sides of a triangle. If a, b, and c are the sides of a triangle, then the perimeter of a triangle is given by the formula:

Perimeter of a triangle = a+b+c units

For example, the sides of a triangle are 3 cm, 4 cm and 5 cm, then the perimeter of a triangle is calculated as:

Perimeter = 3+4+5 cm

Perimeter = 12 cm.

Use this calculator to easily calculate the perimeter of a triangle by the different possible pieces of information.

Quick navigation:

Perimeter of a triangle formula
Rules for solving a triangle
Examples: find the perimeter of a triangle

Perimeter of a triangle formula

The formula for the perimeter of a triangle T is T = side a + side b + side c, as seen in the figure below:

However, given different sets of other values about a triangle, it is possible to calculate the perimeter in other ways. These ways have names and abbreviations assigned based on what elements of the triangle they include: SSS, SAS, SSA, AAS and are all supported by our perimeter of a triangle calculator.

Rules for solving a triangle

So, how to calculate the perimeter of a triangle using more advanced rules? As mentioned above, there are several different sets of measurements you can start with, from which you can solve the whole triangle, meaning you can arrive at the length of its sides as well.

SSS (side-side-side) - this is the simplest one in which you basically have all three sides. Just sum them up according to the formula above, and you are done.
SAS (side-angle-side) - having the lengths of two sides and the included angle (the angle between the two), you can calculate the remaining angles and sides, then use the SSS rule.
SSA (side-side-angle) - having the lengths of two sides and a non-included angle (an angle that is not between the two), you can solve the triangle as well.
ASA (angle-side-angle) - having the measurements of two angles and the side which serves as an arm for both (is between them), you can again solve the triangle fully.

Many of the above rules rely on the Law of Sines and the Law of Cosines, so if you are not familiar with them, it might be a bit tricky to understand them. The law of sines basically states that each side and its opposing angle's sine are related in the same way:

The law of cosines is a generalization of the Pythagorean theorem and states that c2 = a2 + b2 - 2ab·cosγ using the notation from our calculator graph.

Another rule, supported by our perimeter of a triangle calculator is for right-angled triangles only: in such a triangle, if you are given the length of the hypotenuse and one of the other sides, you can easily compute the perimeter using the Pythagorean theorem.

Examples: find the perimeter of a triangle

Example 1: In the simplest scenario one has measured all three sides of a triangle and then it is a matter of simple summation to find the perimeter. For example, if the sides are 3 in, 4 in, and 5 in, then the perimeter is simply 3 + 4 + 5 = 12 inches in total.

Example 2: In a slightly more complicated task, we are given two of the sides and the angle between them. This is then a straightforward application of the SAS rule by replacing the respective values. If sides b and c are equal at 6 feet and the angle is 30° then the length of side a is √b2 + c2 - 2 x b x c x cosα = √36 + 36 - 2 x 6 x 6 x cos(30°) = √72 - 72 x 0.866025 = √72 - 62.3538 = √9.65 = 3.1 ft. The perimeter is then 3.1 + 6 + 6 = 15.1 feet.

How do you find the area of a triangle with coordinates?

The formula of the area of triangle in coordinate geometry is: A = (1/2)|x1 1 (y2 2 − y3 3 ) + x2 2 (y3 3 − y1 1 ) + x3 3 (y1 1 − y2 2 )|, where (x1 1 ,y1 1 ), (x2 2 ,y2 2 ), and (x3 3 ,y3 3 ) are the vertices of triangle.

How do you find the area of a triangle with 3 vertices?

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2.

How do you determine if a triangle is right with coordinates?

Calculate the length of the three sides of the triangle by joining the given coordinates. Let the sides be A, B, and C. The given triangle is right-angled if and only if A² + B² = C².