Question 11.11.2.8: Creating a floor Design A ceramic tile floor is designed in ......
Creating a floor Design
A ceramic tile floor is designed in the shape of a trapezoid 20 feet wide at the base and 10 feet wide at the top. See Figure 7. The tiles, which measure 12 inches by 12 inches, are to be placed so that each successive row contains one fewer tile than the preceding row. How many tiles will be required?
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The bottom row requires 20 tiles and the top row, 10 tiles. Since each successive row requires one less tile, the total number of tiles required is
S=20\,+\,19\,+\,18\,+\,\cdot\cdot\cdot\,+\,11\,+\,10This is the sum of an arithmetic sequence; the common difference is -1. The number of terms to be added is n = 11, with the first term a_{1} = 20 and the last term a_{11} = 10. The sum S is
S={\frac{n}{2}}\left(a_{1}+a_{11}\right)\,={\frac{11}{2}}\left(20\,+\,10\right)\,=\,165In all, 165 tiles will be required.
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