This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the shape of the garden. The shape labelled as "Garden" in the floorplan is a rectangle. Rectangle Step 2: Calculate the area of the garden. From the floorplan: Length of garden = 3.8 m Breadth of garden = 3.1 m The formula for the area of a rectangle is Area = length × breadth. Area of garden = 3.8 m × 3.1 m Area of garden = 11.78 m^2 11.78 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 m Breadth = 3.8 m Area of Bedroom = 3.8 m × 3.8 m = 14.44 m^2 • Area of Open-Plan (Lounge, Kitchen and Dining Area): Length = 4.9 m Breadth = 4.8 m Area of Open-Plan = 4.9 m × 4.8 m = 23.52 m^2 • Area of Bathroom: Length = 1.8 m The total width of the top section is 6 m. The width of the Open-Plan area is 4.8 m. Breadth of Bathroom = 6 m - 4.8 m = 1.2 m Area of Bathroom = 1.8 m × 1.2 m = 2.16 m^2 Next, calculate the total area of the house (excluding the garden, as it's typically not considered part of the "house" structure). Total Area of house = Area of Bedroom + Area of Open-Plan + Area of Bathroom Total Area of house = 14.44 m^2 + 23.52 m^2 + 2.16 m^2 Total Area of house = 40.12 m^2 Finally, calculate the percentage of the house made up of the bedroom: Percentage = (Area of BedroomTotal Area of house) × 100\% Percentage = (14.44 m^240.12 m^2) × 100\% Percentage ≈ 0.3600 × 100\% Percentage ≈ 36.00\% 36.00\% Step 4: Convert 200 millimetres (mm) to metres (m). Given that 1 m = 1000 mm. 200 mm = 200 × 1 m1000 200 mm = 0.2 m 0.2 m Step 5: Calculate the area of one tile in m^2. Each tile is a square with a length and breadth of 200 mm. From Step 4, 200 mm = 0.2 m. The formula for the area of a square is Area = side × side. Area of one tile = 0.2 m × 0.2 m Area of one tile = 0.04 m^2 0.04 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 m^2. • Area of one tile (from Step 5) = 0.04 m^2. • Number of tiles needed for the bedroom: Number of tiles = Area of BedroomArea of one tile Number of tiles = 14.44 m^20.04 m^2 Number of tiles = 361 tiles • Add an additional 5% of tiles: Additional tiles = 361 × 0.05 = 18.05 tiles Total tiles required = 361 + 18.05 = 379.05 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. Number of boxes = (379.05)/(20) Number of boxes = 18.9525 Rounding up to the nearest whole number: Number of boxes = 19 boxes