Math Problem Statement

Calculate the total lineal meters of SKIRTING BOARDS required for the plan below.

Skirtings to all internal walls.

Length "A" 8.529 Meters

Width "A" 5.155 Meters

Length "B" 2.815 Meters

Width "B" 1.623 Meters

Window "A" 1.211 Meters High x 1.740 Meters Wide

Window "B" 1.307 Meters High x 0.877 Meters Wide

Doors 2.100 Meters High x 0.900 Meters Wide

ANSWERS IN METERS TO 3 DECIMAL PLACES

Solution

To calculate the total lineal meters of skirting boards required for the plan, we need to add the perimeter of the walls, while excluding the areas covered by windows and doors. Here's the step-by-step process:

1. Calculate the perimeter of the walls:

For a rectangular space with internal walls, we will first calculate the total length of all walls. The total perimeter of the walls is the sum of the lengths of all the walls.

  • Length "A" = 8.529 meters (two walls of this length)
  • Width "A" = 5.155 meters (two walls of this width)
  • Length "B" = 2.815 meters (two walls of this length)
  • Width "B" = 1.623 meters (two walls of this width)

The total length of the walls:

Perimeter=2×(Length "A"+Width "A"+Length "B"+Width "B")\text{Perimeter} = 2 \times ( \text{Length "A"} + \text{Width "A"} + \text{Length "B"} + \text{Width "B"} )

Substituting the values:

Perimeter=2×(8.529+5.155+2.815+1.623)=2×18.122=36.244meters\text{Perimeter} = 2 \times ( 8.529 + 5.155 + 2.815 + 1.623 ) = 2 \times 18.122 = 36.244 \, \text{meters}

2. Subtract the area of windows and doors:

Now, we'll subtract the areas where the skirting boards won't be required, namely the windows and doors.

  • Window "A" has an area of 1.211m×1.740m=2.104m21.211 \, \text{m} \times 1.740 \, \text{m} = 2.104 \, \text{m}^2
  • Window "B" has an area of 1.307m×0.877m=1.146m21.307 \, \text{m} \times 0.877 \, \text{m} = 1.146 \, \text{m}^2
  • Doors: There are two doors, each with an area of 2.100m×0.900m=1.890m22.100 \, \text{m} \times 0.900 \, \text{m} = 1.890 \, \text{m}^2. So the total area of the doors is 1.890×2=3.780m21.890 \times 2 = 3.780 \, \text{m}^2

However, since skirting boards are typically applied along the edges of walls, we are only concerned with the width of windows and doors for calculation, not their areas. This will give us the lineal distance.

So, the total lineal meters of windows and doors to subtract are:

  • Window "A" width = 1.740 meters
  • Window "B" width = 0.877 meters
  • Doors total width = 2×0.900=1.800meters2 \times 0.900 = 1.800 \, \text{meters}

3. Subtract the lineal meters of windows and doors from the perimeter:

Now, subtract the lineal meters of the windows and doors from the total perimeter:

Total Skirting Length=Perimeter(Window A width+Window B width+Doors total width)\text{Total Skirting Length} = \text{Perimeter} - (\text{Window A width} + \text{Window B width} + \text{Doors total width})

Substituting the values:

Total Skirting Length=36.244(1.740+0.877+1.800)\text{Total Skirting Length} = 36.244 - (1.740 + 0.877 + 1.800)

Total Skirting Length=36.2444.417=31.827meters\text{Total Skirting Length} = 36.244 - 4.417 = 31.827 \, \text{meters}

Final Answer:

The total lineal meters of skirting boards required is 31.827 meters.


Would you like further clarification or details on the calculations?

Related Questions:

  1. How do you calculate the skirting boards if the space includes multiple doors and windows in odd positions?
  2. What factors affect the total skirting board requirement in irregularly shaped rooms?
  3. How do you estimate skirting board costs per meter for a given project?
  4. What materials are most commonly used for skirting boards, and how do they impact installation?
  5. How do skirting boards interact with different types of flooring (e.g., tile, carpet, wood)?

Tip: Always double-check the height of the skirting boards to ensure proper fitting based on the room's interior style.

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Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter Calculation
Area Subtraction

Formulas

Perimeter of rectangle: 2 * (Length + Width)
Area of rectangle: Length * Width
Total skirting length: Perimeter - Sum of widths of windows and doors

Theorems

Area subtraction
Perimeter of a rectangle

Suitable Grade Level

Grades 7-9