Determine the area of an isosceles triangle if the base is 6 cm and the opposite angle is 90 degrees.

Based on the fact that opposite the base, which is 6 cm, lies an angle of 90 degrees, then this triangle is rectangular with a hypotenuse equal to 6 cm and two equal legs. To solve this problem, remember that the area of ​​a right-angled triangle is half the product of the legs of the triangle. Knowing the hypotenuse, we can calculate the legs according to the Pythagorean theorem. Let one leg be equal to x, see Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs. x ^ 2 + x ^ 2 = 6 * 6 2x “2 = 36 x ^ 2 = 36/2 x ^ 2 = 18 x = √18 cm. Knowing that each leg is equal to √18 cm, we calculate the area. S = 1 / 2 * √18 * √18 = 18/2 = 9 cm ^ 2.
Answer: 9 cm ^ 2.