The given figure represents a rectangular lawn on which seven squares numbered from 1 to 7 have been marked. If the area of the smallest of these squares is $1 \mathrm{~m}^{2}$, the total area of the lawn, in $\mathrm{m}^{2}$, is equal to

| 1 | 2 | 5 |  |
| :---: | :---: | :---: | :---: |
|  | 3 |  |  |
|  | 4 |  |  |
|  | 0 |  | 7 |

(a) 42
(b) 44
(c) 45
(d) 48
(e) 49
The correct option is (c).

Solution 1: Since the smaller squares have an area of $1 \mathrm{~m}^{2}$, each of them has a side length of $1 \mathrm{~m}$. From the figure, we conclude that $B C=2 \mathrm{~m}$. Since $A B C D$ is a square, it follows that $B C=C D=A D=2 \mathrm{~m}$. Since $C D E F$ is also a square, we have

$D E=2 \mathrm{~m}$. From the figure, we have

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-038.jpg?height=369&width=554&top_left_y=992&top_left_x=1325)

$$
A H=A B+B H=2+3+5
$$

$E J=A D+D E+A J$ and $A J=A H$. It follows that $E J=2+2+5=9$. Since $E G=A H=5$, the dimensions of the land are $9 \mathrm{~m}$ in length by $5 \mathrm{~m}$ in width. Therefore, its area is $9 \times 5=45 \mathrm{~m}^{2}$.

Solution 2: By gridding the larger rectangle with squares of $1 \mathrm{~m}^{2}$ in area, we obtain the rectangle $B F G H$ formed by 12 squares of $1 \mathrm{~m}^{2}$ in area, the two squares $A B C D$ and $D C F E$ formed by four squares of $1 \mathrm{~m}^{2}$ in area, and the square $A H I J$ formed by 25 squares of $1 \mathrm{~m}^{2}$ in area. Therefore, the area in question

![](https://cdn.mathpix.com/cropped/2024_05_01_666a1aec7e447b0a6cbeg-038.jpg?height=314&width=534&top_left_y=1759&top_left_x=1338)
is $12+4+4+25=45 \mathrm{~m}^{2}$.