A wooden fence 6 ft high and 220 ft long is to be painted on...

A wooden fence 6 ft high and 220 ft long is to be painted on both sides. a. What is the total area to be painted? b. A gallon of a certain type of paint will cover only $200 \mathrm{ft}^{2}$ of area for the first coat, but on the second coat a gallon of the same paint will cover $300 \mathrm{ft}^{2}$. If the fence is to be given two coats of paint, how many gallons of paint should be bought?

A wooden fence 6 ft high and 220 ft long is to be painted on both sides.
a. What is the total area to be painted?
b. A gallon of a certain type of paint will cover only $200 \mathrm{ft}^{2}$ of area for the first coat, but on the second coat a gallon of the same paint will cover $300 \mathrm{ft}^{2}$. If the fence is to be given two coats of paint, how many gallons of paint should be bought?

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Key Concepts

Area Calculation

This concept involves determining the area of a two-dimensional surface by multiplying its length by its height. In the context of painting, accurately computing the total area that needs to be covered is essential for estimating resources.

Surface Area of Multi-faced Objects

When an object has more than one side that requires painting, the surface area calculation must account for each relevant face. For instance, if both sides of a fence need to be painted, the area of one side is calculated and then multiplied accordingly.

Paint Coverage and Efficiency

This key concept pertains to understanding and applying the area that a specific quantity of paint can cover. Different coats or types of surfaces may have varying coverage rates, which must be factored in when calculating the total volume of paint required.

Rounding for Discrete Units

Since paint is typically purchased in whole units (such as gallons), any fractional result from dividing the total area by the coverage rate must be rounded up. This ensures that there is enough paint to completely cover the intended surface without running short.

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