SOLUTION: How to calculate the area of an isosceles right triangle when you only know the length of its hypotenuse???

Algebra ->  Triangles -> SOLUTION: How to calculate the area of an isosceles right triangle when you only know the length of its hypotenuse???       Log On


   

Question 1009450: How to calculate the area of an isosceles right triangle when you only know the length of its hypotenuse???

Found 3 solutions by rothauserc, Fombitz, BashayerNouri:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let s be the side of the given isosceles right triangle, then
s^2 + s^2 = h^2
2s^2 = h^2
s^2 = h^2/ 2
***************************************************************
Area of triangle = (1/2) * s * s
Area of triangle = (1/2) * s^2
Area of triangle = (1/2) * (h^2/2) = (h^2 / 4)


Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
There is a relationship between the hypotenuse and side of this triangle through the Pythagorean theorem.
S%5E2%2BS%5E2=H%5E2
H%5E2=2S%5E2
So then the area of this triangle is,
A=%281%2F2%29%28S%29%28S%29
A=%281%2F2%29S%5E2
Substituting,
A=%281%2F2%29%28H%5E2%2F2%29
A=H%5E2%2F4

Answer by BashayerNouri(2) About Me  (Show Source):
You can put this solution on YOUR website!
Thank you so much rothauserc & Fombit for the help and explanation! Now I understand how to do this problem! :D
I'm greatly appreciated that you took time out of your day to help me.