Area of Isosceles Triangle Formula | Perimeter of a Isosceles Triangle

A triangle is a regular polygon and the closed two-dimensional figure having 3 sides, 3 vertices, and 3 angles. The sum of interior angles adds up to 180 – degree and the sum of the exterior angles would make up 360-degrees.

Three most popular triangles based on the side length are given as –

  1. Equilateral Triangle
  2. Isosceles triangle
  3. Scalene Triangle

In this post, we will discuss the isosceles triangle formula and its area and the perimeter.

Area of Isosceles Triangle Formula

An isosceles triangle is a polygon having two equal sides and two equal angles adjacent to equal sides. Let us discuss further how to calculate the area, perimeter, and the altitude of an isosceles triangle.

Area of Isosceles Triangle Formula

From the figure let a is the side equal for an isosceles triangle, b is the base and h, is the altitude. Then the area of an isosceles triangle formula can be given as –

\[Area\;of\;Isoscele\;Triangle =\frac{1}{2}bh\]

\[Altitude\;of\;an\;Isosceles\;Triangle=\sqrt{a^{2}-\frac{b^{2}}{4}}\]

Where,
b = Base of the isosceles triangle
h = Height of the isosceles triangle &
a = length of the two equal sides

Let us have a quick look at the properties of an isosceles triangle for a better understanding of the concept. These are –

  • The two sides and two base angles are equal.
  • In case, if the third angle is of 90-degree then this is a right isosceles triangle.
  • The length of the sides is equal regardless of the direction of the apex of triangle points.
  • The altitude from the apex to the base bisects the angle at the apex.

The perimeter of an Isosceles Triangle Formula

As discussed earlier, an isosceles triangle has two equal sides and two equal internal angles. If you know the two equal sides and the base side of a triangle then calculating perimeter is easy. The isosceles triangle perimeter formula is given as –

\[\large Perimeter\;of\;Isosceles\;Triangle,P=2\,a+b\]

Where,
a = length of the two equal sides
b = Base of the isosceles triangle

Some facts about the Isosceles Triangle

  1. Cana right triangle be an isosceles triangle too? – Yes, if you halve the square across the diagonal line of the symmetry then angle will make 90-degree and other two will make 45-degree.
  2. Can an equilateral triangle be an isosceles triangle? – For an isosceles triangle, at least two adjacent sides must be congruent. For an equilateral triangle, all three sides are congruent.
  3. Can an isosceles triangle be an equilateral triangle too? – No, because for equilateral triangle we need all three sides equal but this is not the case with the isosceles triangle which has only two congruent sides.
  4. Is an isosceles triangle an example of an acute-angled triangle? – The basic rule for an acute angle triangle is that all three angles should be less than 90-degree. If all three angles of an isosceles triangle are less than 90-degree then it forms an acute-angled triangle otherwise not. For this purpose, you must be sure of the properties of the different type of triangles and check them one by one to satisfy a particular condition.
  5. Is an isosceles triangle an example of an obtuse-angled triangle? – The basic rule for an obtuse angle triangle is that at least one angle should be greater than 90-degrees. If this is the case with an isosceles triangle then it forms an obtuse-angled triangle too.


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