Learning Objectives
- Find area of a room by first converting feet and inches into feet only
- Find price per unit
- Estimate costs using applied geometry
In this section, we will be finding area of rooms in order to determine the cost of flooring and paint. First, we must deal with dimensions that include both feet and inches.
CALCULATING AREA WITH FEET AND INCHES
When calculating the area of a rectangular room, it is important to convert the dimensions into feet only before multiplying.
For example, suppose we want to find the area of a rectangular room that is 12 feet 6 inches by 10 feet 3 inches. This can also be written as:
12 ft. 6 in. x 10 ft. 3 in. or 12′ 6″ x 10′ 3″.
It is important to note that 12′ 6″ is not 12.6 ft. We must first convert to feet only. Using the table below, we see that 12 ft. 6 in. is 12.5 ft. (or 12′ 6″ = 12.5′). Also, 10 ft. 3 in. is 10.25 feet (or 10′ 3″ = 10.25′).
Therefore, to find the area of the rectangular room, we multiply 12.5′ x 10.25′ to get 128.125 square feet (or 128.125 ft2).
We also need to calculate price per unit for items such as fence, base boards, and crown molding. By first finding the perimeter of the shape and then using the price per unit, we can calculate how much that item will cost.
PRICE PER UNIT
If we were to buy 4 oranges for $1.00, the price is $0.25/orange. In this example, the price is $0.25 per orange, which is the price per unit. When finding length, units can be inches, feet, yards, miles, etc. When find area, units can be square inches, square feet, square yards, square miles, etc. Think of the word per as divided by. So, price per unit is price divided by unit.
Example
A certain type of fence cost $931.50 for 75 feet. Find the unit price.
Solution: $931.50/75 feet = $12.42 per foot
The price per foot (unit price) is $12.42.
Try IT
Suppose it cost $1,490.40 to carpet a 144 square foot room. What is the unit price (the cost per square foot)?
Example
Suppose your yard is a 25 ft x 20 ft rectangle. You want to put a fence around the entire yard. Find the price to put up this fence if the price of the fence is $23 per foot, which includes installation.
Solution: You will first need to find the perimeter (the length of the entire fence). The formula for perimeter, P, is:
P = 2 x Length + 2 x Width = 2L + 2W
This fence is 25 feet long, so L = 25 feet. The width is 20 feet, so W = 20 feet. Plugging these numbers into the formula, we get:
P = (2 x 25 feet) + (2 x 20 feet) = 90 feet
Therefore, the fence is 90 feet long. Now, multiply the 90 feet by $23 per foot to get $2,070.
The price to install the 90-foot fence is $2,070.
Try It
Suppose you want to create a rectangular space in your backyard for your dog to be able to run around an play. The dimensions of this space is 15′ 6″ by 12′ 3″. The wire fence you want to install is $2.25 per foot, installed. Find the price to put the fence around this dog space.
Consider this first floor of a house plan.
This is the second floor of the above house.
Examples
Suppose you just moved into the above house. You would like to install new flooring. The carpet you want costs $4.95 per square foot, installed. The tile you want costs $2.28 per square foot, installed.
- You want to carpet Bedrooms 1, 2, and 3, and the Living Room, First Floor Hall, First Floor Closet, Second Floor Hall, Entertainment Room, both Second Floor closets, and the Office.
- You want to install tile in the Kitchen, Dining Room, Laundry Room, and both Bathrooms.
How much will it cost to install the new flooring?
Solution: It is important to stay organized on multiple steps problems such as this. One way is to create a table.
| Rooms for CARPET | Dimensions of Room (Feet and Inches) | Dimensions of Room (Feet only) | Area (Square Feet)
(rounded to the nearest hundredth) |
| Bedroom 1 | 19′ 3″ x 17′ 4″ | 19.25′ x 17.33′ | 333.60 sq ft |
| Bedroom 2 | (same as Bedroom 1) 19′ 3″ x 17′ 4″ | 19.25′ x 17.33′ | 333.60 sq ft |
| Bedroom 3 | 20′ 6″ x 24′ 0″ | 20.6′ x 24′ | 494.40 sq ft |
| Living Room | 19′ 3″ x 25′ 9″ | 19.25′ x 25.75′ | 495.69 sq ft |
| First Floor Hall | 19′ 3″ x 5′ 8″ | 19.25′ x 5.67′ | 109.15 sq ft |
| Second Floor Hall | 30′ 3″ x 8′ 4″ | 30.25′ x 8.33′ | 251.98 sq ft |
| Entertainment Room | 18′ 3″ x 25′ 9″ | 18.25′ x 75′ | 1,368.75 sq ft |
| Small Second Floor Closet | 4′ 8″ x 5′ 0″ | 4.67′ x 5′ | 23.35 sq ft |
| Large Second Floor Closet | 6′ 10″ x 8′ 4″ | 6.83′ x 8.33′ | 56.89 sq ft |
| Office | 11′ 4″ x 24′ 2″ | 11.33′ x 24.17′ | 273.85 sq ft |
| Total | 3,741.26 sq ft |
The carpet is $4.95 per square foot. There are 3,741.26 square feet to be carpeted. We multiply $4.95 x 3,741.26 square feet to get $18,519.24, which is how much it will cost to carpet the specific rooms.
| Rooms for TILE | Dimensions of Room (Feet and Inches) | Dimensions of Room (Feet only) | Area (Square Feet)
(rounded to the nearest hundredth) |
| Kitchen | 26′ 8″ x 16′ 0″ | 26.67′ x 16′ | 426.72 sq ft |
| Dining Room | 17′ 6″ x 16′ 6″ | 17.5′ x 16.5′ | 288.75 sq ft |
| Laundry Room | 11′ 4″ x 14′ 3″ | 11.33′ x 14.25′ | 161.45 sq ft |
| Bathroom 1 | 7′ 2″ x 9′ 10″ | 7.17′ x 9.83′ | 70.48 sq ft |
| Bathroom 2 | (same as Bathroom 1) 7′ 2″ x 9′ 10″ | 7.17′ x 9.83′ | 70.48 sq ft |
| Total | 1,017.88 sq ft |
The tile is $2.28 per square foot. There are 1,017.88 square feet to be tiled. We multiply $2.28 x 1,017.88 square feet to get $2,320.77, which is how much it will cost to tile the specific rooms.
To find the total, sum the carpet cost ($18,519.24) and tile cost ($2,320.77), which is $20,840.01.
This is the end of the section. Close this tab and proceed to the corresponding assignment.
