Perimeter of Triangle

The perimeter of a triangle is the sum of the lengths of all three sides. It is measured in linear units, such as inches, centimeters, or meters. To find the perimeter of a triangle, simply add up the lengths of each side. For example, if a triangle has sides of length 3 inches, 4 inches, and 5 inches, then its perimeter would be 3 + 4 + 5 = 12 inches. The perimeter of a triangle can be used to compare the sizes of different triangles or to calculate the area of a triangle.

Perimeter of an Isosceles, Equilateral and Scalene Triangle

Perimeter of an Isosceles Triangle

An isosceles triangle has two equal sides and one different side. The perimeter of an isosceles triangle is the sum of the lengths of all three sides.

For example, if an isosceles triangle has two sides of length 5 cm and one side of length 3 cm, then its perimeter would be 5 cm + 5 cm + 3 cm = 13 cm.

Perimeter of an Equilateral Triangle

An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of all three sides.

For example, if an equilateral triangle has sides of length 4 cm, then its perimeter would be 4 cm + 4 cm + 4 cm = 12 cm.

Perimeter of a Scalene Triangle

A scalene triangle has all three sides of different lengths. The perimeter of a scalene triangle is the sum of the lengths of all three sides.

For example, if a scalene triangle has sides of length 3 cm, 4 cm, and 5 cm, then its perimeter would be 3 cm + 4 cm + 5 cm = 12 cm.

Perimeter of Right Triangle

A right triangle has a base(b), hypotenuse(h) and perpendicular(p) as its sides, By the Pythagoras theorem, we know,

$h^2 = b^2 + p^2$

Therefore, the Perimeter of a right angle triangle $= b + p + h$

Perimeter, $ P = b + p + \sqrt{b ^ 2 + p ^ 2}$

Examples

Here are some additional examples of how to find the perimeter of different types of triangles:

• An isosceles triangle with sides of length 7 cm and 5 cm has a perimeter of 7 cm + 7 cm + 5 cm = 19 cm.
• An equilateral triangle with sides of length 6 cm has a perimeter of 6 cm + 6 cm + 6 cm = 18 cm.
• A scalene triangle with sides of length 8 cm, 10 cm, and 12 cm has a perimeter of 8 cm + 10 cm + 12 cm = 30 cm.

Solved Examples

Solved Examples

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

Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm and 2 cm.

Solution: Let,

a = 5 cm

b = 4 cm

c = 2 cm

Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11

Therefore, the answer is 11 cm.

Example 2: Find the perimeter of a triangle whose each side is 10 cm.

Solution: Since all three sides are equal in length, the triangle is an equilateral triangle.

i.e. a = b = c = 10 cm

Perimeter = a + b + c

= 10 + 10 + 10

= 30

Perimeter = 30 cm.

Example 3: What is the missing side length of a triangle whose perimeter is 40 cm and two sides are 10 cm each?

Solution: Given,

Perimeter = 40 cm

Length of two sides is the same i.e. 10 cm.

Thus, the triangle is an isosceles triangle.

Using formula: P = 2l + b

40 = 2 * 10 + b

40 = 20 + b

or b = 20

Missing side length is 20 cm.

To learn more about triangles and related topics in Geometry, register with BYJU’S today and sharpen your skills.

Frequently Asked Questions

What does the Perimeter of a Triangle Mean?

The perimeter of a triangle is the total distance around the edges of a triangle. In other words, the length of the boundary of a triangle is its perimeter.

How to Calculate the Perimeter of a Triangle?

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

Here are some additional examples of how to calculate the perimeter of a triangle:

• If the lengths of the three sides of a triangle are 6 cm, 8 cm, and 10 cm, then the perimeter of the triangle is 6 cm + 8 cm + 10 cm = 24 cm.
• If the lengths of the three sides of a triangle are 12 ft, 15 ft, and 18 ft, then the perimeter of the triangle is 12 ft + 15 ft + 18 ft = 45 ft.

Calculate the Perimeter of a Right Triangle with Base as 3 cm and height as 4 cm.

First, using the Pythagorean theorem, calculate the hypotenuse of the right triangle.

$h =\sqrt {base2+perpendicular2}$

$h = \sqrt {32+42}$

$h = \sqrt {9 + 16}$

$ h = \sqrt {25}$

Or, $ h = 5 $ cm

So, the perimeter of the triangle $= 3 + 4 + 5 = 12$ cm.

How to calculate the perimeter of a scalene triangle?

If x, y, and z are the sides of a scalene triangle, then its perimeter formula is given by: Perimeter of a scalene triangle, $P = x + y + z$ units.

Here are some additional examples of how to calculate the perimeter of a scalene triangle:

• If the sides of a scalene triangle measure 3 cm, 4 cm, and 5 cm, then the perimeter is $3 cm + 4 cm + 5 cm = 12 cm.$
• If the sides of a scalene triangle measure 6 cm, 8 cm, and 10 cm, then the perimeter is $6 cm + 8 cm + 10 cm = 24 cm.$
• If the sides of a scalene triangle measure 9 cm, 12 cm, and 15 cm, then the perimeter is $9 cm + 12 cm + 15 cm = 36 cm.$

I hope this explanation helps you understand how to calculate the perimeter of a scalene triangle.

What is the formula for the perimeter of an isosceles triangle?

The perimeter of an isosceles triangle is the sum of the lengths of all three sides. Since an isosceles triangle has two equal sides, we can use the following formula to find its perimeter:

Perimeter = 2(length of equal sides) + length of base

For example, if an isosceles triangle has two equal sides of length 5 cm and a base of length 6 cm, then its perimeter would be:

Perimeter $= 2(5 cm) + 6 cm = 16 cm$

Here are some additional examples of isosceles triangles and their perimeters:

• An isosceles triangle with two equal sides of length 3 inches and a base of length 4 inches has a perimeter of 10 inches.
• An isosceles triangle with two equal sides of length 7 centimeters and a base of length 8 centimeters has a perimeter of 22 centimeters.
• An isosceles triangle with two equal sides of length 10 feet and a base of length 12 feet has a perimeter of 32 feet.

The formula for the perimeter of an isosceles triangle is a simple and straightforward way to find the total length of its sides. By using this formula, you can easily calculate the perimeter of any isosceles triangle, regardless of its size or shape.

What is the formula for the perimeter of an equilateral triangle?

The perimeter of an equilateral triangle is the sum of the lengths of all three sides. Since all sides of an equilateral triangle are equal, we can use the following formula to calculate the perimeter:

Perimeter $= 3$ × side length

For example, if the side length of an equilateral triangle is 5 cm, then the perimeter would be:

Perimeter $ = 3 × 5$ cm $ = 15$ cm

Here are some additional examples:

• If the side length of an equilateral triangle is 8 inches, then the perimeter would be:

Perimeter $= 3 × 8$ inches $= 24$ inches

• If the side length of an equilateral triangle is 10 meters, then the perimeter would be:

Perimeter $= 3 × 10$ meters $= 30$ meters

The formula for the perimeter of an equilateral triangle is a simple and straightforward way to calculate the total length of the triangle’s sides.

Find the perimeter of a triangle whose sides are 3 cm, 4 cm and 6 cm.

Perimeter of a Triangle

The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the sides of the triangle are $3$ cm, $4$ cm, and $6$ cm. So, the perimeter of the triangle is:

$$P = 3 cm + 4 cm + 6 cm = 13 cm$$

title: “Perimeter Of Triangle” weight: 16562059 draft: False

Perimeter of Triangle

The perimeter of a triangle is the sum of the lengths of all three sides. It is measured in linear units, such as inches, centimeters, or meters. To find the perimeter of a triangle, simply add up the lengths of each side. For example, if a triangle has sides of length 3 inches, 4 inches, and 5 inches, then its perimeter would be 3 + 4 + 5 = 12 inches. The perimeter of a triangle can be used to compare the sizes of different triangles or to calculate the area of a triangle.

Perimeter of an Isosceles, Equilateral and Scalene Triangle

Perimeter of an Isosceles Triangle

An isosceles triangle has two equal sides and one different side. The perimeter of an isosceles triangle is the sum of the lengths of all three sides.

For example, if an isosceles triangle has two sides of length 5 cm and one side of length 3 cm, then its perimeter would be 5 cm + 5 cm + 3 cm = 13 cm.

Perimeter of an Equilateral Triangle

An equilateral triangle has all three sides of equal length. The perimeter of an equilateral triangle is the sum of the lengths of all three sides.

For example, if an equilateral triangle has sides of length 4 cm, then its perimeter would be 4 cm + 4 cm + 4 cm = 12 cm.

Perimeter of a Scalene Triangle

A scalene triangle has all three sides of different lengths. The perimeter of a scalene triangle is the sum of the lengths of all three sides.

For example, if a scalene triangle has sides of length 3 cm, 4 cm, and 5 cm, then its perimeter would be 3 cm + 4 cm + 5 cm = 12 cm.

Perimeter of Right Triangle

A right triangle has a base(b), hypotenuse(h) and perpendicular(p) as its sides, By the Pythagoras theorem, we know,

$h^2 = b^2 + p^2$

Therefore, the Perimeter of a right angle triangle $= b + p + h$

Perimeter, $ P = b + p + \sqrt{b ^ 2 + p ^ 2}$

Examples

Here are some additional examples of how to find the perimeter of different types of triangles:

• An isosceles triangle with sides of length 7 cm and 5 cm has a perimeter of 7 cm + 7 cm + 5 cm = 19 cm.
• An equilateral triangle with sides of length 6 cm has a perimeter of 6 cm + 6 cm + 6 cm = 18 cm.
• A scalene triangle with sides of length 8 cm, 10 cm, and 12 cm has a perimeter of 8 cm + 10 cm + 12 cm = 30 cm.

Solved Examples

Solved Examples

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

Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm and 2 cm.

Solution: Let,

a = 5 cm

b = 4 cm

c = 2 cm

Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11

Therefore, the answer is 11 cm.

Example 2: Find the perimeter of a triangle whose each side is 10 cm.

Solution: Since all three sides are equal in length, the triangle is an equilateral triangle.

i.e. a = b = c = 10 cm

Perimeter = a + b + c

= 10 + 10 + 10

= 30

Perimeter = 30 cm.

Example 3: What is the missing side length of a triangle whose perimeter is 40 cm and two sides are 10 cm each?

Solution: Given,

Perimeter = 40 cm

Length of two sides is the same i.e. 10 cm.

Thus, the triangle is an isosceles triangle.

Using formula: P = 2l + b

40 = 2 * 10 + b

40 = 20 + b

or b = 20

Missing side length is 20 cm.

To learn more about triangles and related topics in Geometry, register with BYJU’S today and sharpen your skills.

Frequently Asked Questions

What does the Perimeter of a Triangle Mean?

The perimeter of a triangle is the total distance around the edges of a triangle. In other words, the length of the boundary of a triangle is its perimeter.

How to Calculate the Perimeter of a Triangle?

To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.

Here are some additional examples of how to calculate the perimeter of a triangle:

• If the lengths of the three sides of a triangle are 6 cm, 8 cm, and 10 cm, then the perimeter of the triangle is 6 cm + 8 cm + 10 cm = 24 cm.
• If the lengths of the three sides of a triangle are 12 ft, 15 ft, and 18 ft, then the perimeter of the triangle is 12 ft + 15 ft + 18 ft = 45 ft.

Calculate the Perimeter of a Right Triangle with Base as 3 cm and height as 4 cm.

First, using the Pythagorean theorem, calculate the hypotenuse of the right triangle.

$h =\sqrt {base2+perpendicular2}$

$h = \sqrt {32+42}$

$h = \sqrt {9 + 16}$

$ h = \sqrt {25}$

Or, $ h = 5 $ cm

So, the perimeter of the triangle $= 3 + 4 + 5 = 12$ cm.

How to calculate the perimeter of a scalene triangle?

If x, y, and z are the sides of a scalene triangle, then its perimeter formula is given by: Perimeter of a scalene triangle, $P = x + y + z$ units.

Here are some additional examples of how to calculate the perimeter of a scalene triangle:

• If the sides of a scalene triangle measure 3 cm, 4 cm, and 5 cm, then the perimeter is $3 cm + 4 cm + 5 cm = 12 cm.$
• If the sides of a scalene triangle measure 6 cm, 8 cm, and 10 cm, then the perimeter is $6 cm + 8 cm + 10 cm = 24 cm.$
• If the sides of a scalene triangle measure 9 cm, 12 cm, and 15 cm, then the perimeter is $9 cm + 12 cm + 15 cm = 36 cm.$

I hope this explanation helps you understand how to calculate the perimeter of a scalene triangle.

What is the formula for the perimeter of an isosceles triangle?

The perimeter of an isosceles triangle is the sum of the lengths of all three sides. Since an isosceles triangle has two equal sides, we can use the following formula to find its perimeter:

Perimeter = 2(length of equal sides) + length of base

For example, if an isosceles triangle has two equal sides of length 5 cm and a base of length 6 cm, then its perimeter would be:

Perimeter $= 2(5 cm) + 6 cm = 16 cm$

Here are some additional examples of isosceles triangles and their perimeters:

• An isosceles triangle with two equal sides of length 3 inches and a base of length 4 inches has a perimeter of 10 inches.
• An isosceles triangle with two equal sides of length 7 centimeters and a base of length 8 centimeters has a perimeter of 22 centimeters.
• An isosceles triangle with two equal sides of length 10 feet and a base of length 12 feet has a perimeter of 32 feet.

The formula for the perimeter of an isosceles triangle is a simple and straightforward way to find the total length of its sides. By using this formula, you can easily calculate the perimeter of any isosceles triangle, regardless of its size or shape.

What is the formula for the perimeter of an equilateral triangle?

The perimeter of an equilateral triangle is the sum of the lengths of all three sides. Since all sides of an equilateral triangle are equal, we can use the following formula to calculate the perimeter:

Perimeter $= 3$ × side length

For example, if the side length of an equilateral triangle is 5 cm, then the perimeter would be:

Perimeter $ = 3 × 5$ cm $ = 15$ cm

Here are some additional examples:

• If the side length of an equilateral triangle is 8 inches, then the perimeter would be:

Perimeter $= 3 × 8$ inches $= 24$ inches

• If the side length of an equilateral triangle is 10 meters, then the perimeter would be:

Perimeter $= 3 × 10$ meters $= 30$ meters

The formula for the perimeter of an equilateral triangle is a simple and straightforward way to calculate the total length of the triangle’s sides.

Find the perimeter of a triangle whose sides are 3 cm, 4 cm and 6 cm.

Perimeter of a Triangle

The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the sides of the triangle are $3$ cm, $4$ cm, and $6$ cm. So, the perimeter of the triangle is:

$$P = 3 cm + 4 cm + 6 cm = 13 cm$$