A house floorplan shows a rectangular garden with length 3.8 m and breadth 3.1 m. Calculate its area. Also, determine the percentage of the house area that the bedroom occupies. The bedroom is a squar

Step 1: Identify the shape of the garden.
The shape labelled as "Garden" in the floorplan is a rectangle.

$$\boxed{\text{Rectangle}}$$

Step 2: Calculate the area of the garden.
From the floorplan:
Length of garden $= 3.8 \text{ m}$
Breadth of garden $= 3.1 \text{ m}$
The formula for the area of a rectangle is $\text{Area} = \text{length} \times \text{breadth}$.

$$\text{Area of garden} = 3.8 \text{ m} \times 3.1 \text{ m}$$ $$\text{Area of garden} = 11.78 \text{ m}^2$$ $$\boxed{11.78 \text{ m}^2}$$

Step 3: Calculate the percentage of the entire house made up of the bedroom.
First, calculate the area of each part of the house:

• Area of Bedroom: Length $= 3.8 \text{ m}$ Breadth $= 3.8 \text{ m}$ $$\text{Area of Bedroom} = 3.8 \text{ m} \times 3.8 \text{ m} = 14.44 \text{ m}^2$$
• Area of Open-Plan (Lounge, Kitchen and Dining Area): Length $= 4.9 \text{ m}$ Breadth $= 4.8 \text{ m}$ $$\text{Area of Open-Plan} = 4.9 \text{ m} \times 4.8 \text{ m} = 23.52 \text{ m}^2$$
• Area of Bathroom: Length $= 1.8 \text{ m}$ The total width of the top section is $6 \text{ m}$. The width of the Open-Plan area is $4.8 \text{ m}$. Breadth of Bathroom $= 6 \text{ m} - 4.8 \text{ m} = 1.2 \text{ m}$ $$\text{Area of Bathroom} = 1.8 \text{ m} \times 1.2 \text{ m} = 2.16 \text{ m}^2$$

Next, calculate the total area of the house (excluding the garden, as it's typically not considered part of the "house" structure).

$$\text{Total Area of house} = \text{Area of Bedroom} + \text{Area of Open-Plan} + \text{Area of Bathroom}$$ $$\text{Total Area of house} = 14.44 \text{ m}^2 + 23.52 \text{ m}^2 + 2.16 \text{ m}^2$$ $$\text{Total Area of house} = 40.12 \text{ m}^2$$

Finally, calculate the percentage of the house made up of the bedroom:

$$\text{Percentage} = \left(\frac{\text{Area of Bedroom}}{\text{Total Area of house}}\right) \times 100\%$$ $$\text{Percentage} = \left(\frac{14.44 \text{ m}^2}{40.12 \text{ m}^2}\right) \times 100\%$$ $$\text{Percentage} \approx 0.3600 \times 100\%$$ $$\text{Percentage} \approx 36.00\%$$ $$\boxed{36.00\%}$$

Step 4: Convert 200 millimetres (mm) to metres (m).
Given that $1 \text{ m} = 1000 \text{ mm}$.

$$200 \text{ mm} = 200 \times \frac{1 \text{ m}}{1000}$$ $$200 \text{ mm} = 0.2 \text{ m}$$ $$\boxed{0.2 \text{ m}}$$

Step 5: Calculate the area of one tile in m$^2$.
Each tile is a square with a length and breadth of $200 \text{ mm}$.
From Step 4, $200 \text{ mm} = 0.2 \text{ m}$.
The formula for the area of a square is $\text{Area} = \text{side} \times \text{side}$.

$$\text{Area of one tile} = 0.2 \text{ m} \times 0.2 \text{ m}$$ $$\text{Area of one tile} = 0.04 \text{ m}^2$$ $$\boxed{0.04 \text{ m}^2}$$

Step 6: Calculate how many boxes of tiles are required to tile the bedroom if an additional 5% of tiles are required.

• Area of the bedroom (from Step 3) $= 14.44 \text{ m}^2$.
• Area of one tile (from Step 5) $= 0.04 \text{ m}^2$.
• Number of tiles needed for the bedroom: $$\text{Number of tiles} = \frac{\text{Area of Bedroom}}{\text{Area of one tile}}$$ $$\text{Number of tiles} = \frac{14.44 \text{ m}^2}{0.04 \text{ m}^2}$$ $$\text{Number of tiles} = 361 \text{ tiles}$$
• Add an additional 5% of tiles: $$\text{Additional tiles} = 361 \times 0.05 = 18.05 \text{ tiles}$$ $$\text{Total tiles required} = 361 + 18.05 = 379.05 \text{ tiles}$$
• Tiles are sold in boxes of 20. To find the number of boxes, divide the total tiles required by the number of tiles per box. Since you cannot buy a fraction of a box, round up to the next whole number. $$\text{Number of boxes} = \frac{379.05}{20}$$ $$\text{Number of boxes} = 18.9525$$ Rounding up to the nearest whole number: $$\text{Number of boxes} = 19 \text{ boxes}$$

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