Harold works at a state park. He needs to seal the redwood deck at the information center to protect the wood. He measures the deck and finds that it is a kite with diagonals 40 fe... Harold works at a state park. He needs to seal the redwood deck at the information center to protect the wood. He measures the deck and finds that it is a kite with diagonals 40 feet and 70 feet. Each gallon of sealant covers 400 square feet, and the sealant needs to be applied every six months. How many gallon containers should he buy to protect the deck for the next three years? Read more

Steps to Solve

1. Calculate the Area of the Kite-Shape Deck

The area (A) of a kite can be calculated using the formula:

$$ A = \frac{1}{2} \times d_1 \times d_2 $$

where (d_1) is the length of one diagonal and (d_2) is the length of the other diagonal.

Here, (d_1 = 40) feet and (d_2 = 70) feet.

Plugging in the values:

$$ A = \frac{1}{2} \times 40 \times 70 = 1400 \text{ square feet} $$

2. Determine the Frequency of Sealant Application

Harold needs to apply the sealant every six months. In three years, there are:

$$ \text{Total applications} = \frac{3 \text{ years} \times 12 \text{ months}}{6 \text{ months/application}} = 6 \text{ applications} $$

3. Calculate the Total Area to be Sealed

Since each sealant application covers the total area of the deck, the total area to be sealed over all applications is:

$$ \text{Total area to be sealed} = 1400 \text{ square feet/application} \times 6 \text{ applications} = 8400 \text{ square feet} $$

4. Calculate the Total Gallons of Sealant Needed

Each gallon of sealant covers 400 square feet, so the total number of gallons required is:

$$ \text{Gallons required} = \frac{8400 \text{ square feet}}{400 \text{ square feet/gallon}} = 21 \text{ gallons} $$