The image you uploaded is a Japanese math problem that translates roughly to the following:

"The lower base is 4 cm longer than the upper base, and the height is 5 cm. The area of this trapezoid is 45 cm². Find the lengths of the upper and lower bases of the trapezoid."

Let's denote the following:

• $a$ as the length of the upper base (shorter base).
• $b$ as the length of the lower base (longer base).
• The height $h = 5$ cm.
• The relationship between the bases: $b = a + 4$ cm.
• The area of the trapezoid formula: $A = \frac{1}{2} \times (a + b) \times h$

Substitute the known values: $45 = \frac{1}{2} \times (a + (a + 4)) \times 5$

Simplify: $45 = \frac{1}{2} \times (2a + 4) \times 5$

Multiply both sides by 2 to eliminate the fraction: $90 = (2a + 4) \times 5$

Divide by 5: $18 = 2a + 4$

Solve for $a$: $2a = 18 - 4 = 14$ $a = 7$

Now, using $b = a + 4$: $b = 7 + 4 = 11$

Thus, the upper base $a$ is 7 cm, and the lower base $b$ is 11 cm.

Would you like more details on any steps or have further questions? Here are some related questions:

1. How would the area formula change for a triangle instead of a trapezoid?
2. Can you verify the solution using the area formula again?
3. What if the height of the trapezoid were doubled? How would that affect the bases?
4. Could you find the area if only the upper base was given?
5. What would be the perimeter of this trapezoid with the given values?

Tip: When working with trapezoids, always ensure you know both the height and the relation between the bases to apply the area formula correctly!