Perimeter of a Triangle

We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle.

Perimeter of a triangle is the sum of lengths of its three sides.

Perimeter of a Triangle

For example, perimeter of the ∆PQR = PQ + QR + RP

The perimeter of a triangle ABC

Perimeter of a Triangle

                    = AB + BC + CA

                    = 2 cm + 4 cm + 3 cm,

(add the length of each side of the triangle).

                     = 9 cm

Perimeter of the triangle = Sum of the sides.



Perimeter of a Triangle

● A triangle has 3 sides

The perimeter of the triangle XYZ

= 3 cm + 5 cm + 4 cm

= 12 cm

The perimeter of the triangle = Sum of the lengths of three sides.


Let us consider some of the examples on perimeter of a triangle:

1. Find the perimeter of a triangle having sides 3 cm, 8 cm and 6 cm.

Solution:

Examples on Perimeter of a Triangle

Perimeter of a triangle

                   = Sum of all the three sides

                   = AB + BC + AC

                   = 3 cm + 8 cm + 6 cm

                   = 17 cm


2. Find the perimeter of the triangle PQR whose sides are 4 cm, 6 cm and 8 cm.

Solution:

Perimeter of Triangle

In the figure PQ = 4 cm, PR = 6 cm and QR = 8 cm

The perimeter of the rectangle PQR

                            = 4 cm + 6 cm + 8 cm

                            = 18 cm


3. Find the perimeter of an equilateral triangle whose one side is 5 cm.

Solution:

A triangle in which all the sides are equal is called an equilateral triangle.

Perimeter of the equilateral triangle = 3 × side

                                                    = 3 × 5 cm

                                                    = 15 cm

Thus, perimeter = 15 cm.


4. Find the perimeter of a triangle whose length of three sides are 8 cm, 11 cm, 13 cm.

Solution:

To find the perimeter of the triangle, we add all the sides together.

Perimeter of a triangle

                  = Sum of all the three sides

                  = 8 cm + 11 cm + 13 cm

                  = 32 cm


5. Find the perimeter of a triangle whose sides are 5 cm, 2 cm and 3 cm.

Solution:

Perimeter of the triangle is the sum of the lengths of its sides.

Perimeter = 5 cm + 2 cm + 3 cm

Thus, perimeter = 10 cm.


6. Find the perimeter of each triangle.

Find the Perimeter of each Triangle

Solution: 

(i) Perimeter of ∆XYZ = 5.5 cm + 6 cm + 6 cm = 17.5 cm

(ii) Perimeter of ∆ABC = 8 cm + 6 cm + 6 cm = 20 cm

(iii) Perimeter of ∆PQR = 4 cm + 3 cm + 5 cm = 12 cm


7. Find the perimeter of the given shapes.

Find the Perimeter of the given Shapes

Solution:

(i) Perimeter = PQ + QR + RS + ST + TU + UV + VP

                   = 2.5 cm + 3 cm + 2 cm + 3 cm + 2.5 cm + 4 cm + 4 cm

                   = 21 cm


(ii) Perimeter = PQ + QR + RS + SP

                    = 4 cm + 4 cm + 4 cm + 4 cm

                    = 16 cm


(iii) Perimeter = PQ + QR + RS + ST + TP

                     = 7 cm + 6 cm + 4 cm + 3 cm + 5 cm

                     = 25 cm


8. How to find the perimeter of a triangle?

Find the perimeter of the given triangle.

Find the Perimeter of a Triangle

Solution:

To find the perimeter of a triangle, we measure the three sides of the triangle and add them together.

In the above given figure,

AB = 4 cm

BC = 8 cm and

AC = 7 cm.

Therefore, perimeter of the triangle = 4 cm + 8 cm + 7 cm

                                                   = 19 cm


Word Problems on Perimeter of a Triangle:

1. Two sides of a triangle are 3 cm and 4 cm. Find the third side of the triangle if its perimeter is 11 cm.

Solution:

First side of the triangle                            = 3 cm

Second side of the triangle                        = 4 cm

Perimeter of the triangle                           = Sum of the lengths of sides

i.e. sum of the lengths of the sides            = 11 cm

3 cm + 4 cm + length of the third side      = 11 cm

7 cm + length of the third side                 = 11 cm

But we know that 7 cm + 4 cm                = 11 cm (Note: 11 – 7 = 4)

Therefore, length of the third side            = 4 cm


Worksheet on Perimeter of a Triangle:

1. A triangle has a perimeter of 50 cm. If its two sides are of lengths 15 cm and 19 cm, what is the length of the third side?

Answer: 16 cm


2. Find the perimeter of each of the following triangles:

Worksheet on Perimeter of a Triangle

Answer:

2. (i) Perimeter of the triangle 12 cm.

(ii) Perimeter of the triangle 15 cm.

(iii) Perimeter of the triangle 18 cm.

(iv) Perimeter of the triangle 15 cm.


3. Finding missing side length of the triangle when perimeter is given:

Missing Length of a Triangle

Answer:

3. 5 cm

You might like these

● Related Concepts

Units for Measuring Length

Measuring Instruments

To Measure the Length of a Line-segment

Perimeter of a Figure

Perimeter of a Triangle

Perimeter of a Rectangle

Perimeter of a Square

Unit of Mass or Weight

Examples on Unit of Mass or Weight

Units for The Measurement of Capacity

Examples on Measurement of Capacity

Measurement of Time

Read a Watch or a Clock

Antemeridian (a.m.) or Postmeridian (p.m.)

What Time it is?

Time in Hours and Minutes

24 Hour Clock

Units of Time

Examples Units of Time

Time Duration

Calendar

Reading and Interpreting a Calendar

Calendar Guides us to Know





4th Grade Math Activities

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