Math
Area of Isosceles Triangle Formula  Perimeter of a Isosceles Triangle
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A triangle is a regular polygon and the closed twodimensional 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 360degrees.
Three most popular triangles based on the side length are given as –
 Equilateral Triangle
 Isosceles triangle
 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.
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 90degree 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
 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 90degree and other two will make 45degree.
 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.
 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.
 Is an isosceles triangle an example of an acuteangled triangle? – The basic rule for an acute angle triangle is that all three angles should be less than 90degree. If all three angles of an isosceles triangle are less than 90degree then it forms an acuteangled 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.
 Is an isosceles triangle an example of an obtuseangled triangle? – The basic rule for an obtuse angle triangle is that at least one angle should be greater than 90degrees. If this is the case with an isosceles triangle then it forms an obtuseangled triangle too.

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