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Irene's window store made a mosaic for the community center. The mosaic had a 7×7 array of different color square tiles. If each tile is 1(3)/(4)ft long, what is the area of the whole mosaic?

Irene's window store made a mosaic for the community center. The mosaic had a 7×7 7 \times 7 array of different color square tiles. If each tile is 134ft 1 \frac{3}{4} \mathrm{ft} long, what is the area of the whole mosaic?

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Q. Irene's window store made a mosaic for the community center. The mosaic had a 7×7 7 \times 7 array of different color square tiles. If each tile is 134ft 1 \frac{3}{4} \mathrm{ft} long, what is the area of the whole mosaic?
  1. Calculate Tile Area: Now, we calculate the area of one tile. Area of one tile = (74 ft)×(74 ft)=4916 ft2(\frac{7}{4} \text{ ft}) \times (\frac{7}{4} \text{ ft}) = \frac{49}{16} \text{ ft}^2
  2. Find Total Mosaic Area: Next, we find the total area of the mosaic by multiplying the area of one tile by the total number of tiles in the 7×77\times7 array.\newlineTotal number of tiles = 7×77 \times 7
  3. Calculate Total Tiles: We calculate the total number of tiles.\newlineTotal number of tiles = 7×7=497 \times 7 = 49
  4. Multiply for Mosaic Area: Finally, we multiply the area of one tile by the total number of tiles to get the area of the whole mosaic.\newlineTotal area of the mosaic = Area of one tile ×\times Total number of tiles\newlineTotal area of the mosaic = 4916 ft2×49\frac{49}{16} \text{ ft}^2 \times 49
  5. Calculate Final Mosaic Area: We calculate the total area of the mosaic.\newlineTotal area of the mosaic = 4916 ft2×49=240116 ft2\frac{49}{16} \text{ ft}^2 \times 49 = \frac{2401}{16} \text{ ft}^2

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