Math Problem Statement

There is a wall with length 4 feet 2 inches and height 9 feet. There is a skirting of 4 inches which makes the height 8 feet 8 inches. There is a door with height 6 feet 11 inches and 3 feet 2 inches wide. On the left side of door the wall is 2 1/4 inches and on the right side the wall is 9 3/4 inches. What is the square feet of the wall?

There is a wall with length 4 feet 2 inches and height 9 feet. There is a skirting of 4 inches which makes the height 8 feet 8 inches. There is a door with height 6 feet 11 inches and 3 feet 2 inches wide. On the left side of door the wall is 2 1/4 inches and on the right side the wall is 9 3/4 inches. What is the square feet of the wall?

Solution

Let's calculate the square footage of the wall by breaking it into several components and subtracting the area of the door.

1. Dimensions of the wall:

  • Total height: 9 feet
  • Total width: 4 feet 2 inches = 42124 \frac{2}{12} feet = 4.167 feet

2. Skirting:

  • The height of the skirting is 4 inches, which is 412=0.333\frac{4}{12} = 0.333 feet.
  • This reduces the effective height of the wall to 90.333=8.6679 - 0.333 = 8.667 feet or 8 feet 8 inches.

3. Door dimensions:

  • Height of the door: 6 feet 11 inches = 61112=6.9176 \frac{11}{12} = 6.917 feet
  • Width of the door: 3 feet 2 inches = 3212=3.1673 \frac{2}{12} = 3.167 feet

4. Side wall thickness:

  • Left side wall: 2 1/4 inches = 2.2512=0.1875\frac{2.25}{12} = 0.1875 feet
  • Right side wall: 9 3/4 inches = 9.7512=0.8125\frac{9.75}{12} = 0.8125 feet

Calculation of the Wall Area:

Total wall area:

Total Wall Area=Width×Height=4.167ft×8.667ft=36.12sq ft\text{Total Wall Area} = \text{Width} \times \text{Height} = 4.167 \, \text{ft} \times 8.667 \, \text{ft} = 36.12 \, \text{sq ft}

Door area:

Door Area=Width×Height=3.167ft×6.917ft=21.91sq ft\text{Door Area} = \text{Width} \times \text{Height} = 3.167 \, \text{ft} \times 6.917 \, \text{ft} = 21.91 \, \text{sq ft}

Net Wall Area (subtracting door):

Net Wall Area=Total Wall AreaDoor Area=36.12sq ft21.91sq ft=14.21sq ft\text{Net Wall Area} = \text{Total Wall Area} - \text{Door Area} = 36.12 \, \text{sq ft} - 21.91 \, \text{sq ft} = 14.21 \, \text{sq ft}

Thus, the area of the wall is 14.21 square feet.

Would you like more details or any clarifications?

Here are 5 related questions:

  1. How would adding windows affect the total wall area?
  2. What would be the cost of painting the wall if the rate is $2 per square foot?
  3. How does the skirting size impact the overall wall height?
  4. How would we calculate the area if the wall was a triangle or irregular shape?
  5. What is the perimeter of the door in feet?

Tip: When dealing with mixed units (feet and inches), always convert them to a consistent unit (e.g., feet) for easier calculations.

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Math Problem Analysis

Mathematical Concepts

Area Calculation
Conversions between Feet and Inches
Subtraction of Areas

Formulas

Total Wall Area = Width × Height
Door Area = Width × Height
Net Wall Area = Total Wall Area - Door Area

Theorems

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Suitable Grade Level

Grades 7-9