Final answer:
The area of the trapezoid is irrational because the irrational height (√5 cm) is multiplied by the sum of the rational base dimensions, resulting in an irrational product despite the bases themselves being rational numbers.
Step-by-step explanation:
To find the area of a trapezoid, the formula A = 1/2(b₁+b₂)h is used, where A stands for the area, b₁ and b₂ are the lengths of the two bases, and h is the height. Dylan's question involves calculating the area with given dimensions: b₁ = 3.6 cm, b₂ = 12 1/3 cm (which is a rational number when converted to an improper fraction), and h = √5 cm (an irrational number).
The area of the trapezoid is considered irrational because of option C: the height is irrational, and it is multiplied by the other rational dimensions. Even though both of the base lengths are rational numbers, their sum remains rational; however, when this sum is then multiplied by the irrational height, the result becomes an irrational number.
Let's express 12 1/3 cm as an improper fraction - it becomes 37/3 cm. The sum of the bases is then given by (3.6 cm + 37/3 cm), which is a rational number. When calculating the area, this rational sum is multiplied by the irrational number √5 cm, resulting in an irrational product for the area.