8. CCSS. Reason Abstractly Tiles are being placed in front of a fireplace to create a trapezoidal hearth. The hearth will have a height of 24 inches and bases that are 48 inches and 60 inches. If the tiles cover 16 square inches, how many tiles will be needed?

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1. First, calculate the area of the trapezoidal hearth using the formula for the area of a trapezoid:
   $$
   \text{Area} = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}
   $$

2. Substitute the given values:
   $$
   \text{Area} = \frac{1}{2} \times (48 + 60) \times 24
   $$

3. Simplify the expression inside the parentheses:
   $$
   48 + 60 = 108
   $$

4. Now, calculate the total area:
   $$
   \text{Area} = \frac{1}{2} \times 108 \times 24 = 54 \times 24 = 1296 \text{ square inches}
   $$

5. Each tile covers $$16$$ square inches. Therefore, the number of tiles needed is:
   $$
   \text{Number of tiles} = \frac{1296}{16} = 81
   $$

Thus, $$81$$ tiles will be needed.
81 tiles are needed.

8. CCSS. Reason Abstractly Tiles are being placed in front of a fireplace to create a trapezoidal hearth. The hearth will have a height of 24 inches and bases that are 48 inches and 60 inches. If the tiles cover 16 square inches, how many tiles will be needed?

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