Một hình thang cân có diện tích là 9^2, hiệu độ hai đáy bằng 3 cm

Gọi độ dài đáy nhỏ là x cm và độ dài đáy lớn là y cm.

Theo đề bài, ta có hệ thức diện tích hình thang:

9^2 = (x + y) * 3/2

Simplifying the equation, we have:

81 = (x + y) * 3/2

Multiply both sides by 2/3:

54 = x + y

The problem also states that if the smaller base is increased by 2 cm, the trapezoid will still be a trapezoid and the area will increase by 2^2.

Let's consider the new trapezoid with the smaller base increased by 2 cm. The new smaller base will be x + 2 cm, and the larger base remains y cm.

The new area of the trapezoid is:

(9 + 2)^2 = (x + 2 + y) * 3/2

Simplifying the equation, we have:

121 = (x + 2 + y) * 3/2

Multiply both sides by 2/3:

80.67 = x + 2 + y

Since the area increased by 2^2 = 4, we can set up the following equation:

80.67 - 54 = 4

26.67 = 4

This equation is not true, so our assumption that the smaller base can be increased by 2 cm and the trapezoid will still be a trapezoid is incorrect.

Therefore, there is no solution to this problem.