Let's denote the width of the garden as $w$ meters. According to the problem, the length is 10 meters longer than the width, so the length can be expressed as $w + 10$ meters.

The formula for the perimeter $P$ of a rectangle is:

$P = 2(\text{length} + \text{width})$

Given that the perimeter is 204 meters, we substitute the values:

$204 = 2((w + 10) + w)$

Simplifying:

$204 = 2(2w + 10)$

$204 = 4w + 20$

Subtract 20 from both sides:

$184 = 4w$

Now, divide by 4:

$w = 46$

So, the width of the garden is 46 meters. The length is $w + 10 = 46 + 10 = 56$ meters.

Now, we can calculate the area $A$ of the garden using the formula for the area of a rectangle:

$A = \text{length} \times \text{width} = 56 \times 46$

$A = 2576 \text{ square meters}$

Thus, the area of the garden is 2576 square meters.

Would you like further clarification on any part of this?

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Here are 5 related questions to explore further:

1. How would the area change if the perimeter increased by 20 meters?
2. What if the length was 15 meters longer than the width? How would that affect the area?
3. Can you find the diagonal length of the garden using the Pythagorean theorem?
4. How would the dimensions change if the garden's area were halved?
5. What is the length of the garden if the perimeter was 180 meters instead?

Tip: Always double-check your perimeter and area formulas when solving geometry problems.