Question

In order to estimate the cost of painting a house, a painter needs to know the surface area of the exterior. Develop an algorithm for computing that value, Your inputs are the width, length, and height of the house, the number of windows and doors, and their dimensions. (Assume the windows and doors have a uniform size.)

Short answer

Compute the wall area and subtract the area occupied by windows and doors.

Step-by-step solution

Understand the Problem

The task is to develop an algorithm that calculates the total surface area of a house's exterior, subtracting the areas occupied by windows and doors. We need dimensions of the house and those of windows and doors as inputs.

Identify and List Inputs

The key inputs are: 1. Width (w) of the house 2. Length (l) of the house 3. Height (h) of the house 4. Number of windows (N_w) 5. Number of doors (N_d) 6. Width of a window (w_w) 7. Height of a window (h_w) 8. Width of a door (w_d) 9. Height of a door (h_d)

Calculate Total Surface Area of Walls

Calculate the total surface area of the walls, assuming the house is a rectangular prism:\[ A_{walls} = 2 imes (w imes h) + 2 imes (l imes h) \]

Account for Roof Area (Optional)

If the roof area is to be considered, and it is a flat roof, add:\[ A_{roof} = w imes l \]This will be part of the total surface area unless specified otherwise.

Calculate Window and Door Areas

Compute the total area occupied by windows and doors:1. Window area: \( A_{windows} = N_w imes w_w imes h_w \)2. Door area: \( A_{doors} = N_d imes w_d imes h_d \)

Compute Net Paintable Surface Area

Subtract the total area occupied by windows and doors from the total walls surface area:\[ A_{paintable} = A_{walls} - A_{windows} - A_{doors} \]

Create a Formula Summary

The final formula to compute the paintable surface area is:1. Calculate total wall area: \[ A_{walls} = 2 imes (w imes h) + 2 imes (l imes h) \]2. Calculate areas for windows and doors: \[ A_{windows} = N_w imes w_w imes h_w \] \[ A_{doors} = N_d imes w_d imes h_d \]3. Calculate paintable area: \[ A_{paintable} = A_{walls} - A_{windows} - A_{doors} \]

Key concepts

Surface Area Calculation

Surface area calculation involves determining the total area of the surfaces of a three-dimensional object. In the context of a house, this means calculating the combined area of its exterior walls. Most houses are shaped like a rectangular prism, which greatly simplifies the calculation.

To find the surface area of the walls, you need to consider both the width and length of the house multiplied by its height. The formula used is:

• Multiply the width by the height to get the area of one pair of opposite walls.
• Do the same for the length by the height to get the area of the other pair of opposite walls.
• Add these two results and multiply by two, because there is a pair of each.

So, the formula for the total surface area of the walls is: \[ A_{walls} = 2 \times (w \times h) + 2 \times (l \times h) \] where \( w \) is width, \( l \) is length, and \( h \) is height. This total gives the exterior wall surface area before accounting for windows and doors.

Exterior Painting Estimation

Estimating the amount of paint needed to cover the surface of a house is crucial for budgeting and planning a painting project. After calculating the paintable surface area, the next step is to determine how much paint will be required.

Typically, paint estimations are based on the coverage provided by one gallon of paint. This coverage varies by paint type, but many will cover approximately 350 square feet per gallon. To get an accurate estimate:

• Divide the total paintable surface area by the coverage area provided by a gallon of paint.
• Consider multiple coats if necessary, as some areas may need two or even three coats for full coverage.
• Don’t forget to account for surface texture or previous wall conditions that may affect the paint consumption.

By carefully calculating the surface area and understanding the specific paint's coverage capabilities, you can avoid over-purchasing or under-buying paint. This ensures a smooth and successful painting process.

House Dimensions

Understanding the dimensions of the house is an essential first step in the surface area calculation process. These dimensions include width, length, and height, which define the size and shape of the house.

Every measurement must be as accurate as possible to ensure that the calculated surface area reflects the true area that needs painting. The width and length will be multiplied by the height of the house to find the surface area of each wall.

In addition, when planning for windows and doors:

• Knowing their dimensions will help exclude their areas from the paintable surface.
• A standardized measurement for windows and doors is assumed for easy calculation, commonly known sizes should be used unless otherwise specified.

These precise measurements give a foundational basis for making decisions about material quantities and project scope.

Paintable Surface Calculation

After determining the total exterior wall area, the next step is to calculate the net area that actually requires painting, known as the paintable surface.

This involves accounting for areas that do not need to be painted, such as windows and doors. These elements are subtracted from the overall surface area. Here's how:

• Calculate the area of all windows by multiplying the width and height of one window and then multiplying by the total number of windows.
• Do the same for doors using their width, height, and quantity.

The formula becomes:For windows: \[ A_{windows} = N_w \times w_w \times h_w \] For doors: \[ A_{doors} = N_d \times w_d \times h_d \] The paintable surface area is then:\[ A_{paintable} = A_{walls} - A_{windows} - A_{doors} \] This approach ensures that all non-paintable areas are accurately deducted, giving an exact amount of surface that will require paint.