Problem 3. The figure shown on the right is made of matches (the side of a small square is one match). The area of the entire shaded figure is 300 square centimeters. Find the total length of all the matches used.

![](https://cdn.mathpix.com/cropped/2024_05_06_f96a11c148a7d0414fcdg-1.jpg?height=230&width=242&top_left_y=1451&top_left_x=1114)
Answer: 140 cm.

Solution. Let the area of one small square be $a$. Then, the diagram shows 8 small squares with area $a$ and one large square with area $4a$. The total area is $8a + 4a = 300$, from which $a = 25 \text{ cm}^2$. Therefore, the side of a small square is 5 cm.

Notice that the rectangle formed by two adjacent small squares contains 7 matches. There are 4 such non-overlapping rectangles in the diagram, meaning 28 matches were used. Considering that the length of one match is 5 cm, the total length of all matches is 140 cm.

## Criteria

1 p. Only the correct answer without justification.

2 p. The area of the small square is correctly found, but there is no further progress.

3 p. The length of the match is correctly found, but the answer is not obtained.

4 p. The correct answer and justification are provided.