In a garden, there is a square doghouse with a side length of $1.2 \mathrm{~m}$. From one of its corners, $30 \mathrm{~cm}$ away, on the same side as the entrance, the dog is tied to the outer wall of the doghouse with a 3-meter chain. How large an area can the dog move on?
No matter which direction the dog starts, it can continue moving until its chain hits one of the sides of the doghouse.

The walkable area can be divided into five regions. $T_{1}$ is a semicircle with a radius of $3 \mathrm{~m}$, $T_{2}$ and $T_{3}$ are quarter-circles with radii of $2.7 \mathrm{~m}$ and $2.1 \mathrm{~m}$, respectively. $T_{5}$ is a right triangle, and $T_{4}$ is a sector of a circle. The radius of the sector is $1.5 \mathrm{~m}$, and its central angle, $\alpha$, is equal to one of the acute angles of the right triangle, where

$$
\cos \alpha=\frac{0.9}{1.5}=0.6, \text { hence } \alpha \approx 53.11^{\circ}
$$

The sum of the five areas is:

$$
\frac{3^{2} \pi}{2}+\frac{2.7^{2} \pi}{4}+\frac{2.1^{2} \pi}{4}+\frac{1.5^{2} \cdot 53.11^{\circ} \cdot \pi}{360^{\circ}}+\frac{0.9 \cdot 1.2}{2} \approx 24.9091 \mathrm{~m}^{2}
$$

If the area of the doghouse is also included, the total walkable area is $26.3491 \mathrm{~m}^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_02_9544607007ef520abe2bg-1.jpg?height=536&width=569&top_left_y=735&top_left_x=781)