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The problem asks us to find the area of the entire rectangle, which has been divided into seven squares, as shown in the diagram. The smallest square has an area of 1.

To solve this, let's follow these steps:

1. **Identify the side length of the smallest square:** Since the smallest square has an area of 1, its side length is \(\sqrt{1} = 1\).

2. **Label the squares based on their side lengths:** If we label the squares according to their increasing size, the smallest square's side length is 1. From the arrangement of squares in the diagram, it's clear that each subsequent square's side length is a sum of the preceding squares' side lengths.

3. **Determine the side lengths of all squares:**
   - There are three squares of side length 1 (including the smallest one).
   - There is one square with side length 2 (since its side is made up of two 1-sized squares).
   - There is one square with side length 3 (since its side is made up of three 1-sized squares).
   - There is one square with side length 4 (since its side length is 1 + 3).
   - The largest square has a side length of 5 (since its side length is 1 + 4).

4. **Calculate the side lengths of the rectangle:**
   - The width of the rectangle is the sum of the side lengths of the squares aligned horizontally: \(4 + 1 = 5\).
   - The height of the rectangle is the sum of the side lengths of the squares aligned vertically: \(3 + 2 = 5\).

5. **Calculate the total area of the rectangle:**
   - Since the rectangle's dimensions are 5 (width) and 5 (height), the total area is \(5 \times 5 = 25\).

Therefore, the total area of the rectangle is **25** square units.

Would you like more details on any of the steps, or do you have any questions?

Here are some related questions you might find interesting:
1. How would the area change if the smallest square had a different area?
2. Can this arrangement be done with a different number of squares?
3. What if the side lengths of the squares followed a different pattern?
4. How do the side lengths change if the squares increase geometrically instead of arithmetically?
5. What are the properties of shapes when divided into equal-area sections?

**Tip:** When working with areas of geometric shapes, always check if you can simplify calculations by finding patterns in dimensions or using known geometric properties.

Stačiakampį padalino į septynis kvadratus taip, kaip parodyta brėžinyje. Mažiausio kvadrato plotas lygus 1. Raskite viso stačiakampio plotą.

Learn how to find the area of a rectangle divided into seven squares with a detailed explanation. The smallest square has an area of 1, and the problem uses basic geometry concepts like square areas and rectangle dimensions. Suitable for students in Grades 7-9.

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