Answer: Therefore, the area of the isosceles right triangle is approximately 81,329.50 square units.
Step-by-step explanation:In an isosceles right triangle, the two legs are of equal length. Let's assume that each leg has length x. Then, by the Pythagorean theorem, we have:
hypotenuse^2 = leg^2 + leg^2
Substituting the values given in the problem, we get:
570^2 = x^2 + x^2
Simplifying and solving for x, we have:
2x^2 = 570^2
x^2 = (570^2)/2
x ≈ 403.01
So, each leg of the triangle has a length of approximately 403.01.
The area of an isosceles right triangle is (leg^2)/2. Substituting the value of x, we have:
Area = (403.01^2)/2
Area ≈ 81,329.50 square units
Therefore, the area of the isosceles right triangle is approximately 81,329.50 square units.