Question

What is the area of an isosceles right triangle with hypotenuse `6sqrt2`?

Answer 1

Since its a right isosceles triangle we have from Pythagoras' theorem

that

`a^2+a^2=(6sqrt2)^2=>2a^2=36*2=>a=6`

Hence the triangle has sides `6,6,6sqrt2`

Using Heron formula we can calculate the Area

`A=sqrt(s*(s-a)*(s-b)*(s-c))`

where `s=(a+b+c)/2`

a,b,c the sides of the triangle