# Isosceles Triangle Perimeter Formula

## Isosceles Triangle Perimeter Formula

The sum of all the sides makes up the perimeter of an isosceles triangle, which is the length of its whole border. If a triangle has two equal sides and two equal angles, it is said to be an isosceles triangle. Using examples that have been solved, students can learn more about the Isosceles Triangle Perimeter Formula.

## Perimeter of Isosceles Triangle

An Isosceles Triangle Perimeter Formula is equal to the sum of its three sides. The circumference of an isosceles triangle is equal to twice the equal side plus the different side since it has two equal sides. Linear units like inches (in), yards (yd), millimetres (mm), centimetres (cm), and metres are used to measure it (m). In the next part, students may learn the formula for calculating Isosceles Triangle Perimeter Formula.

As is common knowledge, a shape’s border determines its perimeter. Similar to this, the perimeter of an isosceles triangle is determined by adding up its three sides. If students know the base and side of an isosceles triangle, they can calculate the Isosceles Triangle Perimeter Formula. The Isosceles Triangle Perimeter Formula is as follows:

The Isosceles Triangle Perimeter Formula is P = 2a + b units, where an is the length of the triangle’s base and b is the length of its two equal sides.

The region that an Isosceles Triangle Perimeter Formula occupies in two dimensions is referred to as its area. Typically, the base and height of an isosceles triangle are divided by two to create the triangle. The following Isosceles Triangle Perimeter Formula may be used to determine an isosceles triangle’s area:

An Isosceles Triangle Perimeter Formula area is given by the formula A = 12 b h square units, where b is the base and h is the height.

Three sides and three vertices make up a triangle. Students can categorise the triangle as an equilateral triangle, isosceles triangle, or scalene triangle depending on how long the sides are. Each side of an equilateral triangle is equal. Any two sides of an Isosceles Triangle Perimeter Formula are equal, however, all three sides of a scalene triangle are distinct. Students can get a detailed explanation of the Isosceles Triangle Perimeter Formula.

The Greek words “peri” and “metron,” which both imply surrounding and measure, are combined to get the English term perimeter.

The Isosceles Triangle Perimeter Formula of any form is its overall collection of edges. Any polygon’s perimeter is equal to the sum of its side lengths. The length of a closed figure’s boundary or outer line is referred to as its perimeter, with the exception of polygons.

Right-angled triangles are triangles having one right angle. Students are aware that a right angle is 90 degrees. Two straight angles cannot exist in a triangle because the total of the three angles equals 180 degrees. The triangle’s longest side, or hypotenuse, is the side that faces the 90-degree angle. The total of the other two angles, which each have a smaller angle than 90 degrees will be 90 degrees.

In an isosceles right-angled triangle, the hypotenuse and two sides are identical. An isosceles right triangle has two equal angles that are 45 degrees apart.

By calculating the total length of all sides, one may get the perimeter of an Isosceles Triangle Perimeter Formula. The Isosceles Triangle Perimeter Formula right triangle is given by: where the lengths of the two equal sides are and the length of the hypotenuse is h units.

𝑃=ℎ+𝑙+𝑙

### Perimeter of Isosceles Right Triangle

The sum of the lengths of the three sides of an isosceles right-angled triangle represents its perimeter. As a right-angled triangle, it has three equal sides and a hypotenuse on one of its sides. The perimeter of an isosceles right triangle would be: Perimeter of isosceles right triangle = h + l + l if the hypotenuse is h units long and the other two sides are l units long. Students who need help understanding the proportions and Isosceles Triangle Perimeter Formula right triangle might look at the illustration provided on the Extramarks website and mobile application.

One of the most fascinating shapes students will ever have the opportunity to examine is the Isosceles Triangle Perimeter Formula. This is a very engaging topic and includes a lot of patterns and intriguing Isosceles Triangle Perimeter Formula from which they may learn a lot. Triangles are ubiquitous, and the patterns they are connected with are as widely dispersed. They are all around humans, yet understanding them requires careful study. Exyramarks’ experts advise students to try to relate the information they gain from this page to their everyday life as they observe the items around them and consider the triangle’s symmetry.

A right isosceles triangle has two equal sides, one of which serves as the triangle’s base and the other as its perpendicular. The third uneven side is referred to as the hypotenuse. The Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular, may thus be used in Isosceles Triangle Perimeter Formula.

The total length of all the sides adds up to the perimeter of an isosceles triangle. The Isosceles Triangle Perimeter Formula is equal to the sum of the lengths of the other side plus twice the lengths of the two similar sides. Units including millimetres (mm), inches (in), yards (yd), centimetres (cm), metres (m), and others can be used to measure the perimeter.

### Examples on Perimeter of Isosceles Triangle

• Example 1: If the base is 6 cm and one of the equal sides is 10 cm long, what is the perimeter of an isosceles triangle?

Solution:

One can use the Isosceles Triangle Perimeter Formula to get an isosceles triangle’s perimeter: perimeter = 2a plus b. In this instance, one equal side (a) is 10 cm long, and base (b) is 6 cm long.

Make the following substitutions in the formula: = 2 (10) + 6 = 20 + 6

The given isosceles triangle has a 26 cm perimeter.

• Example2: Calculate the perimeter of a right triangle with an isosceles hypotenuse of 8 units.

Solution: The perimeter of an isosceles right triangle may be computed using the formula perimeter of isosceles right triangle = h(1 + √2) when just the hypotenuse is available.

The result of replacing h = 8 is that the isosceles right triangle’s perimeter is given by h(1 + √2) = 8(1 + √2) units.

• Example 3: A triangle field has sides that are 16, 25, and 35 metres long. Calculate the price of fencing the field’s perimeter at a cost of ₹15 per metre.

Solution: Given, the triangle’s three sides measure 16 metres, 25 metres, and 35 metres, respectively.

The formula for the triangle’s perimeter may be used to determine the length of the triangular field’s border.

So, 16 m plus 25 m plus 35 m, or 76 m, is the measurement of the triangular field’s perimeter.

The price of fencing a 1-meter boundary is now assumed to be ₹15.

Therefore, 76 x 15 = ₹1140 is the cost of fencing a 76-meter-long boundary.

Having three vertices, three edges, and three internal angles, a triangle is a three-sided polygon. A triangle, then, is a closed two-dimensional shape having three sides and three angles. Based on the sides and angles, triangles are divided into many categories. Each of them has unique characteristics of its own.

### Practice Questions on the Perimeter of Isosceles Triangle

Q.1

In an isosceles triangle with equal sides of 13 inches each and the third side of 7 inches, calculate the perimeter.

Options

A. 36 – inches

B. 33 – inches

C. 34 – inches

D. 24 – inches

Q2.

An isosceles triangle with two equal sides of 10 inches each and a perimeter of 37 inches has to have a third side that is how long?

Responses

A. 16 Inches

B. 17 inches

C. 20 inches