**Isosceles Triangle Perimeter Formula**

The lengths of the two sides are equal in an isosceles. In an isosceles triangle, the two angles opposite equal sides are equal in size.

The following are the types based on their sides:

- Scalene Triangle
- Equilateral Triangle
- Isosceles Triangle

The lengths of the two sides are equal in an isosceles triangle. In an isosceles triangle, the two angles opposite equal sides are equal in size.

If the sides AB and AC of an ∆ ABC are equal, then ∆ ABC is an isosceles triangle with sides B = C.

The theorem defines the isosceles triangle and states, “If the two sides of a triangle are congruent, then the angle opposite them is also congruent.”

**Properties of Isosceles Triangle:**

- Since the two sides of this triangle are equal, the uneven side is the triangle’s base
- The angles opposite the triangle’s two equal sides are always equal
- From the base to the vertex (topmost) of an isosceles triangle
- A right isosceles triangle has 90 degrees as its third angle

**Isosceles Triangle Theorem: **

If the triangle has two equal sides, it is said to be isosceles. If the triangle is congruent, then the angles opposing two congruent sides are also congruent; if two angles are congruent, then the sides opposite them are also congruent, according to the theorem.

In the triangle, ABC as shown above,

AC = AB.

∠ABC = ∠ADC

**Area of Isosceles Triangle:**

The area of an isosceles triangle in two-dimensional space is defined as the area it occupies.

Area = ½ × base × height square units

**The perimeter of the Isosceles Triangle:**

The perimeter of any shape is the shape’s boundaries, as we all know.

Perimeter = 2a + b units

**Examples:**

- How do you calculate the area of an isosceles triangle with a height of 6 cm and a base of 4 cm?

It is given here that,

Base = 4 cm

Height = 6 cm

Now, the area is 1/2× base × height square units.

Now, put the values of base and height in the formula.

A = 1/2 × 4 × 6 = 12 cm2

Hence, the area of an isosceles triangle is 12 cm2.

- Calculate the perimeter of an isosceles triangle with a 6 cm wide and a 4 cm base.

Here, Base = 4 cm

The length of the two equal arms is given as 6 cm.

Now, P = 2a + b units

Now, put the values of a and b in the perimeter formula.

P = 2(6) + 4

= 12 + 4

= 16 cm