Work the following area application problem.
You are given the job of laying carpet for a six-story building. At each floor the dimensions of the floor are 75 meters in length by 40 meters in width. A stairwell takes up a space 2.5 m by 1.5 m, and cuts through each floor. If the rest of the floor area is to be carpeted, how much carpeting will you need?
Total area =
To find the total area of the carpeting needed, we first need to calculate the area of each floor excluding the stairwell, and then multiply it by the number of floors.
1. Calculate the area of each floor excluding the stairwell:
The dimensions of the floor are given as 75 meters in length and 40 meters in width. Since the stairwell cuts through the floor, we need to subtract its area from the total floor area.
The area of the floor (without the stairwell) can be calculated as:
Floor area = Length × Width - Stairwell area
Stairwell area = Stairwell length × Stairwell width
Stairwell area = 2.5 m × 1.5 m
Floor area = 75 m × 40 m - 2.5 m × 1.5 m
Floor area = 3000 m² - 3.75 m²
Floor area = 2996.25 m²
2. Calculate the total area of carpeting needed:
Since there are six floors in the building, we multiply the floor area by the number of floors.
Total area of carpeting needed = Floor area × Number of floors
Total area of carpeting needed = 2996.25 m² × 6
Total area of carpeting needed = 17,977.50 m²
Therefore, you will need a total of 17,977.50 square meters of carpeting to cover the floors of the six-story building.