Area Of Isosceles Triangle

What is an isosceles triangle?

An isosceles triangle is one which has at least two sides of equal length.  This property is equivalent to two angles of the triangle being equal. An isosceles triangle, therefore, has both two equal sides and two equal angles. The name derives from the Greek iso (same) and Skelos (leg). An equilateral triangle is a special case of the isosceles triangle where all the three sides and angles of the triangle are equal.

Isosceles Triangle

Because the isosceles triangle has two equal side lengths and two equal angles where those sides meet the third line, it is a symmetrical shape. If a perpendicular line is drawn from the point of intersection of two equal sides to the base of the unequal side, two right angle triangles are generated.

Area of isosceles triangle

An isosceles triangle area can be calculated using the formula given below:

Let the length of the base of the triangle be 2a. Divide the base into two halves.

 Isosceles Triangle

using pythagoras theorem

c2 = a2 + b2

b = √(c2 – a2)

we know that the area of  right angle triangle is given by

       =    1/2 * base * height

area is    =  1/2 *a * √(c2 – a2)

therefore total area of an isosceles triangle is = 2*  1/2 *a * √(c2 – a2)

= a * √(c2 – a2)

Area of isosceles right triangle formula:

 Isosceles Triangle

area = 1/2 * base * height

area = 1/2 * a *a = a2/2

the perimeter of an isosceles right triangle is the sum of all the sides of an isosceles right triangle.

Suppose the two equal sides are a. Using Pythagoras theorem the unequal side is found to be a√2.

Hence,

perimeter of isosceles right triangle =  a+a+a√2

= 2a+a√2

= a(2+√2)

= a(2+√2)


Practise This Question

Which point is interior to ABC?