Problem 9.4. From left to right, intersecting squares with sides $12, 9, 7, 3$ are depicted respectively. By how much is the sum of the black areas greater than the sum of the gray areas?

![](https://cdn.mathpix.com/cropped/2024_05_06_d7ec6e60d14a8fdbf750g-34.jpg?height=686&width=872&top_left_y=927&top_left_x=289)
Answer: 103.

Solution. Let's denote the areas by $A, B, C, D, E, F, G$.

![](https://cdn.mathpix.com/cropped/2024_05_06_d7ec6e60d14a8fdbf750g-35.jpg?height=751&width=975&top_left_y=107&top_left_x=239)

We will compute the desired difference in areas:

$$
\begin{aligned}
A+E-(C+G) & =A-C+E-G=A+B-B-C-D+D+E+F-F-G= \\
& =(A+B)-(B+C+D)+(D+E+F)-(F+G)= \\
& =12^{2}-9^{2}+7^{2}-3^{2}=103
\end{aligned}
$$