A 45° -45° - 90° right triangle has hypotenuse of length h. What is th

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As the triangle is a 45-45-90 triangle , it is called isosceles right triangle with the 2 sides (perpendicular and the base) equal in length.

Let 'a' be the length of the perpendicular and the base. h is given to be height of the triangle.

Apply pythagoras theorem to get,

\(a^2+a^2=h^2\) ---> \(2a^2=h^2\)---> \(a^2=\frac{h^2}{2}\) ....(1)

Now, the area of the triangle = A = 0.5*perpendicular*base = 0.5*a*a=\(0.5*a^2\) .....(2)

Now substitute the value of \(a^2\) from (1) in (2), we get

A = \(0.5*\frac{h^2}{2}\) = \(\frac{h^2}{4}\) .

E is the correct answer.

Hope this helps.