Final answer:
The area of an isosceles triangle inscribed in a circle with the base as the diameter is 256 cm². The radius of the circle is used as both the height of the triangle and the length of the radius, with the diameter acting as the base.
Step-by-step explanation:
Given that the base of an isosceles triangle in this problem is the diameter of the circle, we can deduce that the triangle is a right triangle (by Thales' theorem). The diameter forms the hypotenuse of the triangle, and the other two sides are equal in length since it's an isosceles triangle. The radius of the circle is given as 16 cm, so the diameter is 2 × 16 cm = 32 cm.
The area of a triangle is given by the formula: Area = 1/2 × base × height. The base of our triangle is 32 cm (the diameter), and the height will be the same length as the radius, which is 16 cm, because the altitude in a right triangle that is also an isosceles triangle will be equal to the radius of the circumscribed circle.
Therefore, the area of the triangle is:
Area = 1/2 × 32 cm × 16 cm
= 1/2 × 512 cm²
= 256 cm²
So, the area of the triangle inscribed in the circle is 256 cm².