Question

Sandra and Jerry Hampton built a deck in the shape of a regular hexagon off the back of their new home. The sides of the hexagon are 14 feet long. The couple has decided to apply water sealant to the surface of the deck to protect it from the elements. The Hamptons have already spent more than they had planned on for their new deck and they have only $30 left of their budget. The couple needs to determine the total area of the deck in order to know how much sealant to buy. What is the area of the Hampton's deck?

The couple finds that one gallon of the sealant covers 180 square feet. How many gallons will Sandra and Jerry need?

If the best price the Hamptons could find for water sealant was $12.49 per one-gallon can, will they be above or below their $30 budget?

Answer 1

The area of the Hampton's deck is 756 * sqrt(3) square feet. They will need approximately 4.2 gallons of sealant. The total cost will exceed their $30 budget, as it will be approximately $52.47.

Step-by-step explanation:

The area of a regular hexagon can be found using the formula:

Area = 3 * sqrt(3) * s^2 / 2

where s is the length of one side of the hexagon.

In this case, the length of one side of the hexagon is 14 feet. Plugging this value into the formula:

Area = 3 * sqrt(3) * (14^2) / 2

Simplifying the equation:

Area = 756 * sqrt(3) square feet

In terms of gallons of sealant required, the couple needs to divide the area of the deck by the coverage area of one gallon of sealant. In this case, each gallon covers 180 square feet:

Number of gallons required = Area / Coverage area of one gallon

Number of gallons required = 756 * sqrt(3) / 180

Calculating this, they will need approximately 4.2 gallons of sealant.

Finally, to determine if the couple is above or below their $30 budget, the couple needs to multiply the number of gallons required by the price per gallon:

Total cost = Number of gallons required * Price per gallon

Total cost = 4.2 * $12.49

The total cost will exceed their $30 budget, as it will be approximately $52.47.

Answer 2

Answer: The Hamptons will be above their $30 budget.

Step-by-step explanation:

A hexagon is a SIX sided shape. We can assume that the deck has FIVE sides that need to be covered with sealant as it has been built OFF the back of the house.

Part 1:

The total surface area of the deck will be the area of one side multiplied by 5 using the following formula:

A=3sqrt3(side)^2 ×5

A=3sqrt3(14ft)^2 ×5

A=2546.1ft^2

Part 2:

By using cross multiplication and the given information that 1 gallon of sealant covers 180 square feet we can calculate the total amount of gallons needed by the Hamptons like this:

180ft^2/180ft^2 = 2546.1ft^2gal/180ft^2

to find that the gallons needed by the Hamptons are 14.1 gallons.

Part 3:

The best price the Hamptons found allows them to get 1 gallon for $12.49 which means they can only buy 2 gallons with their $30 budget ($30÷$12.49=2 gallons). However this is insufficient as they need 14.1 gallons.