The Perimeter and Area formulas used for any triangle is also true for an isosceles triangle.

Perimeter P = (a + b + c) units, where a, b and c represent the lengths of the triangle ABC.

In the case of an isosceles triangle two sides are of equal length, say b = c.

Hence the formula can be refined as: Perimeter P = a + 2b

The general area formula used for calculating the area of a triangle

Area = $\frac{1}{2}$ x base x height.

The Heron formula also used for calculating the area of a triangle

Δ = $\sqrt{s(s-a)(s-b)(s-c)}$

where s is the semi perimeter of the triangle and s = $\frac{a+b+c}{2}$

The formula can be simplified for an isosceles triangle where b = c as,

Δ = (s - b) $\sqrt{s(s - a)}$ and s can also be taken as s = $\frac{a}{2}$ + b.In the case of as isosceles right triangle, using Pythagorean theorem, a relationship between the lengths of the legs and the hypotenuse can be written as:

c^{2} = a^{2}^{} + b^{2} where c is the length of the hypotenuse and a and b are the lengths of the legs.

In case of an isosceles right triangle a = b = x (say)

Hence c^{2} = x^{2} + x^{2} = 2x^{2}.

⇒ c = $\sqrt{2}$x.

In other word the length of hypotenuse in a 90-45-45 special right triangle is $\sqrt{2}$ times the length of the leg.

This result can be applied to the length of the diagonal of a square as, the length of the diagonal of a square is $\sqrt{2}$ times the side length.