geometry

Fin side length  

s^2 + s^2 = 4^2
2s^2 = 16

s = sqrt 8

area = 1/ 2   Base * height 

        = 1/2   Sqrt8   * sqrt 8  =  4 units²

So the first thing to notice is that it is a 45 - 45 - 90 right triangle.

This means that the ratio of the sides are 1 - 1 - \(\sqrt2\)

This means that one leg has the length of\(4\over\sqrt2\) which simplifies to \(2\sqrt2\)

Now because it is a right triangle, you get \(\frac{1}{2} \times 2\sqrt2 \times 2\sqrt2\)

So the answer is 4.

In a certain isosceles right triangle, the altitude to the hypotenuse has length 4. What is the area of the triangle?

Area = 4²