SOLUTION: Been struggling with this one, Jack renovating his kitchen and has decided to use tiles on his counter-top which is 83cm by 203cm. The tiles are octagonal and square in a patter

Question 1062175: Been struggling with this one,
Jack renovating his kitchen and has decided to use tiles on his counter-top which is 83cm by 203cm. The tiles are octagonal and square in a pattern where four octagons around one square. The square tiles are 3cm along one side.
(a) Estimate the number of tiles they will need to cover the counter-top.
(b) Each square tile costs $0.55 and each octagonal tile costs $0.78. Estimate the cost of the tiles to cover the counter-top.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
I assume that we have regular octagon tiles
:
area of square = 3 * 3 = 9 cm^2
:
the octagon is a square with the corners cut off, each corner is a 45 - 45 -90 right triangle
:
the hypotenuse is 3cm, then calculate the length of a side
:
s^2 + s^2 = 3^2
:
2s^2 = 3^2
:
s = square root(3^2 / 2) = 3 / square root(2) = 1.5 * square root (2)
:
length of the octagon square = ( 3 + 2 * ( 1.5 * square root (2) )
:
area of octagon square = ( 3 + 3 *square root (2) )^2 = 9 + 18 * square root(2) + 18 = 27 + 18 * square root(2)
:
area of triangles = 4 * ( (1/2) * (3/2)square root(2) * (3/2)square root(2) ) = 9
:
area of octagon = 27 + 18square root(2) - 9 = 18(1 + square root(2)) = 43.46 cm^2
:
area of counter-top = 83 * 203 = 16849 cm^2
:
The area of the square and 4 octagon system = 9 + 4 * 43.46 = 182.84
:
There are 16849 / 182.84 = 92.2 approximately 92 systems
:
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There are 92 squares and 4 * 92 = 368 octagons
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:
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Total cost = 92 * 0.55 + 368 * 0.78 = $337.64
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