If the hypotenuse of a right-angled isosceles triangle is 2cm , what is the area of the triangle?

If the hypotenuse of a right-angled isosceles triangle is 2cm , what is the area of the triangle?

Answer Details

An isosceles triangle has two equal sides and two equal angles opposite those sides. In a right-angled isosceles triangle, the two equal angles are 45 degrees each, since the sum of all angles in a triangle is 180 degrees and the right angle is 90 degrees. Let's use the Pythagorean theorem to find the length of the legs of the triangle. If the hypotenuse is 2cm, then each leg is x cm. Applying the Pythagorean theorem, we have: x^2 + x^2 = 2^2 2x^2 = 4 x^2 = 2 x = sqrt(2) Therefore, the length of each leg of the triangle is sqrt(2) cm. To find the area of the triangle, we can use the formula: Area = (base * height) / 2 Since the triangle is isosceles, the base and height are equal. Therefore, we can use either leg as the base and the other leg as the height. Area = (sqrt(2) * sqrt(2)) / 2 Area = 2 / 2 Area = 1 cm^2 So, the area of the right-angled isosceles triangle is 1 cm^2.