Question

ron has 4 - inch square tiles that he will use to tile the area around fireplace, as shown in the diagram below. 8 inches 4 feet fireplace 8 inches 4 feet how many tiles does ron need to tile the area shown? 6 of 10 quest 48 34 40 44

Explanation:

Step1: Convert feet to inches

Since \(1\) foot \( = 12\) inches, \(4\) feet \(=4\times12 = 48\) inches.

Step2: Calculate the area of the large square

The side - length of the large square is \(48\) inches. The area of a square is \(A = s^{2}\), so \(A_{large}=48\times48=2304\) square inches.

Step3: Calculate the area of the fireplace (rectangle)

The dimensions of the fireplace: one side is \(48 - 8=40\) inches (subtracting the non - fireplace part from the side of the large square), and the area of a rectangle is \(A = l\times w\). So \(A_{fireplace}=40\times40 = 1600\) square inches.

Step4: Calculate the area to be tiled

\(A = A_{large}-A_{fireplace}=2304 - 1600=704\) square inches.

Step5: Calculate the area of one tile

The tile is a square with side \(s = 4\) inches. The area of a square is \(A=s^{2}\), so \(A_{tile}=4\times4 = 16\) square inches.

Step6: Calculate the number of tiles

The number of tiles \(n=\frac{A}{A_{tile}}=\frac{704}{16}=44\).

Answer:

44