The homeowners decide on an octagonal deck with all sides thesame length and per
ID: 3092807 • Letter: T
Question
The homeowners decide on an octagonal deck with all sides thesame length and perimeter of 128 feet. The perpendiculardistance from the center of the deck to any side is about 19feet. They will build the deck themselves. the productused to seal the wood surface of the deck is painted on and comesin one-gallon cans. Each gallon of sealing product covers 125square feet. Draw a diagram of the problem situation. Then find the number of gallons of sealant that the homeowners willneed to seal the deck with one and twocoats. please help don't understand this problem
Explanation / Answer
Since they tell you the perimeter of the octagon is 128 feet. You have that each side is 16 feet (128 / 8 sides).Then you try to find the area of the octagon. You knowthat it is 19 feet from the center. What I would do isseparate the octagon into 8 triangles. The formula to findthe area of a triangle is A = 1/2 * base * height. The baseis 16 feet and the height is 19. This means that the area forone of the triangles is (1/2)*(16)*(19) which is 152. So thearea of the octagon is 1216 square feet (8 triangle in octagon *152). It says that each gallon of sealant covers 125 feet. So for one coating you would take the area of the octagon anddivide it by 125. Then for 2 coats just take your answer forthe one coat and multiply it by two.
I hope this makes sense.
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