# How do you find the area of a isosceles triangle with base 10 and perimeter 36?

##### 2 Answers

The area is

#### Explanation:

Giving us the perimeter of an isosceles triangle means we are indirectly given the lengths of the three sides.

If the base is

The equal sides are therefore

To find the area of the triangle we need its height.

the height of an isosceles triangle can be found from its line of symmetry. If you cut the triangle into two identical triangles, for each we will have:

A

A base of

The hypotenuse is

You can therefore use Pythagoras' Theorem to find the third side which will be the height of the triangle.

You might recognise that these are two values of the Pythagorean Triple,

If not you can work it out.

Now we know that the height is

#### Explanation:

Let;

Recall;

Firstly;

Substituting the values..

#26 = 2s

Therefore, slant height is

Also recall;

Using Pythagoras theorem;

Since we are using pythagoras theorem, the base of the triangle would be halved..

Therefore,

Substituting the values..

Hence;

Substituting the values..