Let’s solve the problem step by step.

Part (a): Calculate the shaded area of the floor plan

We will divide the shape into distinct regions and calculate their areas individually. The dimensions are:

1. Main rectangular area (A1):

   • Dimensions: $12 \, \text{ft} \times 5 \, \text{ft}$
   • Area: $A_1 = 12 \times 5 = 60 \, \text{ft}^2$

2. Triangular areas (A2 and A3):

   • Each triangle has a base of $5 \, \text{ft}$ and a height of $5 \, \text{ft}$.
   • Area of one triangle: $A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 5 = 12.5 \, \text{ft}^2$
   • Total for both triangles: $A_{\text{triangles}} = 2 \times 12.5 = 25 \, \text{ft}^2$

3. Bench area (to subtract):

   • Dimensions: $5 \, \text{ft} \times 2 \, \text{ft}$
   • Area: $A_{\text{bench}} = 5 \times 2 = 10 \, \text{ft}^2$

4. Storage closet area (to subtract):

   • Dimensions: $2 \, \text{ft} \times 2 \, \text{ft}$
   • Area: $A_{\text{closet}} = 2 \times 2 = 4 \, \text{ft}^2$

Total shaded area:

$\text{Total shaded area} = A_1 + A_{\text{triangles}} - A_{\text{bench}} - A_{\text{closet}}$ $\text{Total shaded area} = 60 + 25 - 10 - 4 = 71 \, \text{ft}^2$

Part (b): Determine the number of tiles required

1. Tile size:

   • Each tile measures $2 \, \text{ft} \times 2 \, \text{ft}$, so the area of one tile is: $\text{Tile area} = 2 \times 2 = 4 \, \text{ft}^2$

2. Number of tiles needed (without waste): $\text{Number of tiles} = \frac{\text{Total shaded area}}{\text{Tile area}} = \frac{71}{4} = 17.75 \, \text{tiles}$ Round up to 18 tiles.

3. Adding 10% for waste:

   • Waste adjustment: $18 \times 1.1 = 19.8 \, \text{tiles}$
   • Round up to 20 tiles.

Part (c): Determine the cost of tiles

1. Boxes required:

   • Each box contains 8 tiles.
   • Number of boxes: $\text{Number of boxes} = \lceil \frac{\text{Total tiles}}{\text{Tiles per box}} \rceil = \lceil \frac{20}{8} \rceil = 3 \, \text{boxes}$

2. Cost per box:

   • Each box costs $13.99.
   • Total cost: $\text{Total cost} = 3 \times 13.99 = 41.97$

Final Answers:

• (a) Shaded area: $71 \, \text{ft}^2$
• (b) Total tiles needed: $20 \, \text{tiles}$
• (c) Total cost: $41.97$ (excluding tax)

Would you like further details or clarifications? Here are five related questions:

1. How do you calculate the area of composite shapes?
2. Why is it necessary to account for waste in tiling projects?
3. What would the total cost be including a sales tax of, for example, 8%?
4. How would the solution change if the tiles were 1 ft by 1 ft instead?
5. Can you explain why rounding up is necessary when working with tiles?

Tip: Always measure your area carefully, as errors in initial calculations can lead to unnecessary extra costs!