The roof of the house shown needs to be reshingled. a)...

The roof of the house shown needs to be reshingled. a) Considering that the front and back sections of the roof have equal areas, find the total area to be reshingled. b) If roofing is sold in squares (each covering $100 \mathrm{ft}^{2}$ ), how many squares are needed to complete the work? c) To remove old shingles and replace with new shingles costs $\$ 97.50$ per square. What is the cost of reroofing?

The roof of the house shown needs to be reshingled.
a) Considering that the front and back sections of the roof have equal areas, find the total area to be reshingled.
b) If roofing is sold in squares (each covering $100 \mathrm{ft}^{2}$ ), how many squares are needed to complete the work?
c) To remove old shingles and replace with new shingles costs $\$ 97.50$ per square. What is the cost of reroofing?

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Key Concepts

Surface Area Calculation

This concept involves determining the total area of all surfaces that require a particular treatment, such as applying new shingles. In construction and geometry, accurate surface area calculation is essential for estimating material requirements and project scope.

Unit Conversion for Material Quantities

Materials in construction are often sold using specific units that represent a defined area, such as a 'square' in roofing. Understanding how to convert between the units used in design and those used in material sales is crucial for ensuring that the correct amount of material is ordered.

Rounding Up in Material Estimation

When purchasing construction supplies, materials are typically sold in whole units. This necessitates rounding up any calculated quantity to the next whole unit to avoid shortages, even if the calculated requirement is fractional.

Cost Estimation in Construction Projects

This involves multiplying the quantity of material or number of units by their cost per unit to determine the total project cost. Accurate cost estimation is a key aspect of budgeting and financial planning in construction projects.

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