B3. The courtyard has a floor plan of the shape shown in the figure:

![](https://cdn.mathpix.com/cropped/2024_06_07_64c08af683227112c601g-3.jpg?height=368&width=560&top_left_y=1869&top_left_x=174)

A. Write an expression (with the variable $a$) for the perimeter of the shape and simplify it.

B. Write an expression (with the variable $a$) for the area of the shape and simplify it.

C. We want to tile the courtyard with square tiles of dimensions $20 \mathrm{~cm} \times 20 \mathrm{~cm}$. What is the minimum number of tiles needed if $a=2 \mathrm{~m}$?
B3. The perimeter of a shape is the sum of the lengths of all its sides: $2 a+a+$ $a+2 a+\frac{a}{2}+2 a+\frac{3 a}{2}+a+a+a+4 a=17 a$. The area of the courtyard is divided into smaller rectangles, for example, as shown in the figure. The area of the shape is the sum of the areas of these four rectangles: $S=S_{1}+S_{2}+S_{3}+S_{4}=2 a \cdot a+4 a \cdot a+2 a \cdot \frac{a}{2}+a \cdot a=$ $2 a^{2}+4 a^{2}+a^{2}+a^{2}=8 a^{2}$

If $a=2 \mathrm{~m}$, the area of the courtyard is $S=8 \cdot(2 \mathrm{~m})^{2}=32 \mathrm{~m}^{2}$. The area of one tile is $20 \mathrm{~cm} \cdot 20 \mathrm{~cm}=400 \mathrm{~cm}^{2}=0.04 \mathrm{~m}^{2}$. For tiling the courtyard, we would need at least $\frac{32 \mathrm{~m}^{2}}{0.04 \mathrm{~m}^{2}}=$

![](https://cdn.mathpix.com/cropped/2024_06_07_64c08af683227112c601g-6.jpg?height=377&width=577&top_left_y=1573&top_left_x=1342)
800 tiles.

A. The simplified expression for the perimeter of the shape $17 a$ $2 \mathrm{t}$

B. The simplified expression for the area of the shape $8 a^{2}$ $2 \mathrm{t}$

C. The calculated area of the courtyard $32 \mathrm{~m}^{2}$. $1 \mathrm{t}$

The calculated area of one tile $0.04 \mathrm{~m}^{2}$ $1 \mathrm{t}$

The calculated number of tiles: 800 or the written answer. $1 \mathrm{t}$