Formulas for Isosceles Triangles
In geometry, an isosceles triangle is a triangle having two sides of equal length. The two angles opposite to the equal sides are equal and are always acute. Various formulas for isosceles triangles are explained below. The two important formulas for isosceles triangles are the area of a triangle and the perimeter of a triangle.
What Are the Formulas for Isosceles Triangles?
Area of an Isosceles Triangle: It is the space occupied by the triangle and is the and here we have three formulas to find the area of a triangle, based on the given parameters.

Area = 1/2 × Base × Height

Area = \(\dfrac{b}{2}\sqrt{\text{a}^2  \dfrac{b^2}{4}}\)
(Here a is the equal side, and b is the base of the triangle.) 
Area = 1/2 ×abSinθ
(Here a and b are the lengths of two sides and θ is the angle between these sides.)
Perimeter of an Isosceles Triangle: In an isosceles triangle, there are three sides: two equal sides and one base. Here the length of the equal side is s and the length of the base is b. In order to calculate the perimeter of an isosceles triangle, the expression 2s + b is used,
P = 2s + b
Let us check a few examples to more clearly understand the use of formulas for isosceles triangles.
Solved Examples Using Formulas for Isosceles Triangles

Example 1: Determine the area of an isosceles triangle that has a base 'b' of 8 units and the lateral side 'a' of 5 units?
Solution: Applying Pythagora's theorem:
a^{2} = (b/2)^{2} + h^{2}
h^{2} = a^{2}  (b/2)^{2} = 5^{2}  4^{2} which gives h = 3
Area 'A' = (1/2) x b x h = (1/2) 8×3 = 12 unit^{2}
Answer: The area of an isosceles triangle is 12 unit^{2}.

Example 2: Find the lateral side of an isosceles triangle with an area of 20 unit^{2} and a base of 10 units?
Solution: Using the formula of area of an isosceles triangle:
A = (1/2) b h = 20
Given b = 10,
To find: lateral side
h = 40 / 10 = 4
Applying Pythagora's theorem:
a^{2} = (b/2)^{2} + h^{2} = √ ( 5^{2} + 4^{2}) = √41
Answer: The lateral side of an isosceles triangle is √41.