4. Variant 1.

The figure shows a rectangle composed of twelve squares. The perimeter of this rectangle is 102 cm. What is its area? Express your answer in square centimeters.

![](https://cdn.mathpix.com/cropped/2024_05_06_9d8fa1da0443074cdbacg-3.jpg?height=290&width=485&top_left_y=1476&top_left_x=774)
Answer: 594.

Solution. We will call the squares large (one such), medium (three such), and small (eight such). Let's denote the side of the medium square as $4a$. Then the side of the large square is $12a$, and the side of the small squares is $12a: 4=3a$. Therefore, the sides of the rectangle are $12a$ and $4a+12a+3a+3a=22a$, and the perimeter is $2(12a+22a)=68a \cdot a=102: 68=\frac{3}{2}$. The area is $12a \cdot 22a=264a^{2}=66 \cdot 9=594$.