What is an Isosceles Triangle

Isosceles Triangle

The triangle having two sides of equal length is called isosceles triangle. Another way ..., the triangle that has two equal length of sides is called isosceles triangle.

Vertex Angle

The angle included by the two equal legs or sides of an isosceles triangle is an vertex angle.

The vertex for the vertex angle opposite the base is sometimes called the appex.

Base Angles

In an isosceles triangle, the angles included by one of the legs (or equal sides) and the base are base angles.

One can determine all angles depending upon a given angle for an isosceles triangle.

Although there is a seperate formula to finding out the area of an isosceles triangle, but one can also evaluate the area applying the formula used for scalene triangle.

Perimeter of Isosceles Triangle

The sum of base and twice the equal side of an isosceles triangle is called the perimeter.

Let BC = b, AC = a and AB = a in an isosceles △ABC.

Then the perimeter,

P = (a + a + b) unit

∴ P = (2a+b) unit

Area of Isosceles Triangle

Suppose, base BC = b, AC = a and AB = a in an isosceles △ABC.

Draw AD⊥BC.

The perpendicular drawn from the vertex to base divides the base into two equal parts.

∴ BD = 12 BC

∴ BD = b2

From the right △ABD, it can be written as

AD² = AB² - BD²

or, AD² = ‍a² - b²4

or, AD² = 4a² - b²4

or, AD = √4a² - b²√4

or, AD = √4a² - b²2

∴ △ABC = 12 BC.AD

or, △ABC = 12 b. √4a² - b²2

∴ △ABC = b4 √4a² - b²