Final answer:
The area of the trapezoid is irrational due to the multiplication of a rational number (the average of the bases) with the irrational number that is the height (square root of 5), as per the area formula for a trapezoid.
Step-by-step explanation:
The area of the trapezoid is irrational because it involves the multiplication of a rational number by the square root of an irrational number, which results in an irrational number.
In Dylan's scenario, he is given the lengths of the bases of the trapezoid as 3.6 cm and 12 1/3 cm, and the height as the square root of 5. The formula for the area of a trapezoid is A = 1/2(b1+b2)h. The first base, b1 = 3.6 cm (a rational number), and the second base, b2 = 12 1/3 cm (also a rational number). However, the height, h, is the square root of 5, which is an irrational number.
When calculating the area, the sum of the bases (which is a rational number) is multiplied by 1/2 (also rational) and then by the square root of 5 (irrational), which yields an irrational result.