Isosceles Triangles Formula

Isosceles Triangles Formula

In the study of geometry, a triangle is said to be isosceles if its two sides are of similar length. Both of the angles that are perpendicular to the parallel sides have the same degree of acuteness and are always identical. 

Another characteristic of an isosceles triangle is that its two sides will meet at right angles to the base, the third side. 

What are all the isosceles triangle formulas?

The formulae for calculating the area of a triangle and the perimeter of a triangle are two of the most significant ones for isosceles triangles. The various formulas are as mentioned below:

• The perimeter of an isosceles triangle

The perimeter of an isosceles triangle consists of the three sides that make up the triangle: the base, two sides that are equal in length, and the third side, which is the base. To determine the length of the perimeter of an isosceles triangle, the formula 2a + b is used.

P = 2a + b

Here, the length of the side equal to the base is denoted by a, whereas the length of the base is denoted by b.

• Area of an isosceles triangle

The area of an isosceles triangle refers to the total space that the triangle takes up in its environment. Following are three different equations that may be used to calculate the area of a triangle depending on the information that has been provided.

1. Area = 1/2 × Base × Height
2. Area = b/ 2√(a2−b2/4)
   The triangle’s base is denoted by the letter b, and the equal side is denoted by the letter a.
3. Area = 1/2 ×abSinα
   (Here, a and b denote the lengths of two different sides, and the angle formed by these two lengths is denoted by α.)

• Isosceles Triangle Height: 

The height of an isosceles triangle is equal to the perpendicular of the line that runs from the triangle’s apex to the base of the triangle. The formula h = ( √a2–b2/4) is used as a calculation tool to determine the altitude of an isosceles triangle.

Solved examples 

• Calculate Find the area, altitude, and perimeter of an isosceles triangle. Its two equal sides are of length 4 cm and the third side is 6 cm.

Given

a = 4 cm 

b = 6 cm

P = 2× a + b

P = 2× 4 + 6

= 14 cm

Therefore the perimeter will be 14 cm.

•  Find the area of an isosceles triangle given its height as 4 cm and base as 5 cm?

Given that,

Base = 5 cm and height = 4 cm

We know that,

Area of an isosceles triangle is ½ × b × h

A = ½ × 5 × 4 = 20 cm2