Area of an Isosceles Triangle

The area of an isosceles triangle is calculated from the base b (the non-repeated side) and the height (h) of triangle corresponding to the base. The area is the product of the base and the altitude divided by two, being its formula the following one:

How is it obtained?

The area of isosceles triangle is obtained as the base product (side b) by height (h) divided by two (Note: why is the area of a triangle half of the base product by height?).

This can be calculated from Pythagorean theorem. The sides a, b/2 and h form a right angled triangle. The sides b/2 and h are the legs and a the hypotenuse.

The altitude h corresponding to the base is obtained by the following calculations:

The height (altitude) (h) will be:

It is applied that area is a half of the multiplication of base (b) by height (h):

The formulaof area of isosceles triangle is reached.

Exercise

Determine the area of a isosceles triangle knowing its two equal sides (a=3 cm) and the unequal one, whose length is 2 cm (b=2 cm).

What is its area?

Calculate the area using the above formula by multiplying the base by the height:

The area of this isosceles triangle is 2.83 cm².

Table of Triangle Area Formulas

You can see the table of triangle area formulas . Depending on the type of triangle you may need one element ( equilateral triangle), two (base and height) or three (as long as they are not the three angles).