A wooden fence 6 ft. high and 300 ft. long is to be painted. How many gallons of paint are...

Question:

A wooden fence 6 ft. high and 300 ft. long is to be painted.

How many gallons of paint are needed if one gallon covers 400 sq. ft.?

Area of a Rectangle:

In mathematics, a rectangle is a two-dimensional shape with four sides, such that opposite sides are parallel and congruent, and the sides meet at 90° angles. The area of a rectangle (i.e. the amount of space inside the rectangle) is equal to the length of the rectangle times the width of the rectangle, giving the formula {eq}Area=length \times width {/eq}.

Answer and Explanation:

To determine how many gallons of paint will be needed to cover the fence, we will first find the area of the fence, and then, since 1 gallon covers 400 square feet of fence, we will divide our total derived fence area by 400. The problem states that the length of the rectangular fence is 300 feet and that its width (or height) is 6 feet. Thus, the area of the fence will be 300 times 6.

  • {eq}Area = 300 \times 6=1800 {/eq}

We therefore find that the area of the fence is 1800 square feet. Since 1 gallon of paint covers 400 square feet, we determine the number of gallons needed to paint the fence by dividing 1800 by 400.

  • {eq}1800 \div 400 = 4.5 {/eq}

We've therefore concluded that we will need 4.5 gallons of paint to cover the fence.


Learn more about this topic:

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Measuring the Area of a Rectangle: Formula & Examples

from Geometry: High School

Chapter 8 / Lesson 7
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