Final answer:
To calculate the area of the isosceles trapezoid, we need to find the height, which cannot be determined using the side lengths provided. Without additional information or assumptions, we cannot proceed with the area calculation or select an answer.
Step-by-step explanation:
The question asks for the area of an isosceles trapezoid with sides of lengths 4 cm, 10 cm, 16 cm, and 10 cm. To find the area of this trapezoid, we must recognize that the lengths of 10 cm and 16 cm represent the lengths of the two parallel sides (bases), and the other two lengths of 4 cm each are the non-parallel sides.
Using the formula for the area of a trapezoid, which is Area = ½(height)(sum of the bases), we first need to determine the height of the trapezoid. This can be done by drawing a height from one of the bases perpendicular to the opposite base. Since this is not a right trapezoid, the height is not immediately evident, so we need to employ the Pythagorean theorem to find it.
However, without the height, we cannot calculate the area with the information provided. We may try to determine it if we assume that the trapezoid is not only isosceles but also right, meaning that the height and one of the non-parallel sides form a right angle. Still, the information given is not sufficient to guarantee a single solution without additional data or assumptions. Therefore, without the height or a way to calculate it, we cannot accurately select any of the answer choices from A to D.