Find the perimeter of the triangle whose vertices calculator

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

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1. Perimeter of a triangle formula
2. Rules for solving a triangle
3. 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:

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.

Find perimeter of a triangle on a coordinate plane with coordinates A(-3,6), B(-3,2) and C(3,2) rounded off to 2 decimals places.

Answer

Verified

Hint:In the given question, we need to calculate the perimeter of a triangle whose coordinates of vertices are given to us. In such types of questions, we have to first find the lengths of sides of the triangle using distance formula and then sum up the distances to find the perimeter of the required triangle.

Complete step by step answer:
Perimeter of a triangle $ = $ sum of all sides.
So, we need to find the lengths of sides, namely AB, BC and CA.
Using distance formula,
Distance between two points whose coordinates are given as\[({x_1},{y_1})\] and \[({x_2},{y_2})\] is given as $\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} $.
So, distance between A and B = $AB = \sqrt {{{( - 3 - ( - 3))}^2} + {{(2 - 6)}^2}} $
 $ = AB = \sqrt {0 + 16} $
$ = AB = 4$units
Distance between B and C = $BC = \sqrt {{{(3 - ( - 3))}^2} + {{(2 - 2)}^2}} $
 $ = BC = \sqrt {36 + 0} $
 $ = BC = 6$units
Distance between C and A = $CA = \sqrt {{{( - 3 - 3)}^2} + {{(6 - 2)}^2}} $
$ = CA = \sqrt {36 + 16} $
$ = CA = \sqrt {52} $
$ = CA = 2\sqrt {13} $
$ = CA = 2 \times 3.6055$
$ = CA = 7.21{\text{ }}$units (rounded off up to two decimal places)
So, perimeter of triangle ABC $ = AB + BC + CA$
Perimeter of triangle ABC $ = \left( {4 + 6 + 7.21} \right)$ units
Perimeter of triangle ABC $ = 17.21{\text{ }}$units.
So, the perimeter of the triangle on a coordinate plane with coordinates A(-3,6), B(-3,2) and C(3,2) rounded off to 2 decimals places is $17.21{\text{ }}$ units .

Note: The given triangle in the problem is a right angled triangle as side AB is along the x axis and side BC is along the y axis. So, the side CA can also be calculated using the Pythagoras theorem and then the perimeter of triangle ABC can be evaluated by adding up all the sides.

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