Any closed two-dimensional shape can be calculated by adding up its lengths on each of its sides. The perimeter of any closed shape is defined as the distance around the shape. Whenever we draw a polygon, we measure its perimeter by adding its sides. The final answer must always contain units.
For example, if the sides of the triangle are measured in centimeters, the answer should be also expressed in centimeters. When calculating the perimeter of closed-form figures, the formulas usually depend upon how long the outside lines are? Thus, the perimeter of triangle will be determined by its three sides.
The formula for the perimeter of a triangle:
Perimeter = Sum of the three sides
Example: What is the perimeter of a triangle with sides of 6 inches, 2 inches, and 8 inches
Ans: Perimeter of triangle = Sum of all sides
= (6 + 2 + 8) inches
= 16 inches
Therefore, the answer is 16 inches.
This principle is the same for all triangles.
Finding the perimeter of a right-angled triangle
- When side lengths are given, add them together.
- Solve for a missing side using the Pythagorean theorem.
- If we know side-angle-side information, solve for the missing side using the Law of Cosines.
Perimeter according to different types of triangles:
1. Isosceles triangle: Two sides of the isosceles triangle are equal
Perimeter = 2a + c
Example: In triangle ABC, 2 sides of the triangle (a) = 10 cm & Base (c) = 5 cm. Find the perimeter of the triangle.
Ans: Perimeter = 2(10) + 5
= 25 cm
2. Equilateral triangle: All three sides of an equilateral are equal.
Perimeter = 3x (x is the length of each side of the triangle)
Example: Find the perimeter of an equilateral triangle of sides 4 cm
Ans: Perimeter = 3x
Perimeter= 3×4= 12 cm
3. Scalene triangle: All sides of a scalene triangle are unequal.
Perimeter = s + l + m
Example: In a given triangle ABC, find the perimeter for a given triangle having three sides of 20 cm, 30 cm, 40 cm.
Ans: perimeter = (20 + 30+ 40) cm = 90 cm
Following are some of the most common uses of the perimeter of the triangle in real life:
- Whenever the individuals need to fence of the area to plot a particular crop and the area is triangular in shape then they need to have a clear-cut idea about the perimeter to find out the fencing required.
- Whenever the individuals have to undertake the construction of any kind of area then they need to pour the concrete into the foundation which will also be based upon utilisation of the formulas related with perimeter so that everything can be perfectly planned out.
- Building the box stalls for horses is directly linked with having clear access to the right kind of building material. For this purpose moving with proper planning is very much vital and having an idea about the perimeter formula is vital to indulge into accurate calculations at every step.
- Utilisation of the formula of perimeter can also be undertaken very easily whenever the people have to install the traffic signs because they are normally in triangular shape.
Sailing boat is also based upon utilisation of the triangular perimeter formulas so that taking can be perfectly undertaken and everybody will be able to travel forward with the wind at the right angles to the boat.
- In the cases of roof of the houses sometimes triangular shape has to be planned by the people and for this purpose calculation of the area as well as perimeter is another very important aspect to be undertaken in the whole process.
- In the case of staircase and ladder it is very much important for the people to be clear about the perimeter formula so that accurate decisions are always made in the whole process.
The formula for the perimeter of a right triangle:
There are three sides to the triangle, with the longest being the hypotenuse, the base, and the perpendicular depending on the angle taken. Adding the base and perpendicular leg lengths of a right-angled triangle, then adding the hypotenuse, gives the perimeter.
So, the perimeter of right-angle triangle = a + b + c
Where a and b are two legs of right angle and c is the opposite side of the right angle, also called the hypotenuse.
The Pythagorean Theorem is used to find the length of a missing side when the lengths of the sides are not given. As a result, the squares of both sides of a right angle should be added to get the square of the hypotenuse.
The Pythagorean Theorem a2 + b2 = c2
The perimeter can only be calculated in terms of a and b if the values of any two sides (base and perpendicular) are known:
P = a + b + √ (a2 + b2)
Where a and b are the two legs of the triangle.
Several essential applications exist in agricultural fields, such as determining the fields’ dimensions and computing the land required for agriculture. If you want to learn more about a scalene triangle, you can check out Cuemath, one of the best online platforms to learn math and coding.