To find the area of the pizza that was eaten, we'll first calculate the area of the entire pizza and then find the proportion of that area corresponding to the 150-degree angle.
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Calculate the radius of the pizza: \[ \text{Diameter} = 12 \text{ inches} \quad \Rightarrow \quad \text{Radius} = \frac{12}{2} = 6 \text{ inches} \]
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Calculate the area of the whole pizza using the formula for the area of a circle: \[ \text{Area} = \pi r^2 = \pi (6^2) = \pi (36) = 36\pi \text{ square inches} \]
Using \(\pi \approx 3.14\): \[ \text{Area} \approx 36 \times 3.14 = 113.04 \text{ square inches} \]
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Calculate the fraction of the pizza that was eaten based on the angle: The total angle in a circle is 360 degrees. The fraction of the pizza that corresponds to 150 degrees is: \[ \text{Fraction eaten} = \frac{150}{360} = \frac{5}{12} \]
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Calculate the area of the pizza that was eaten: \[ \text{Area eaten} = \text{Total area} \times \text{Fraction eaten} = 113.04 \times \frac{5}{12} \]
Calculate \(113.04 \times \frac{5}{12}\): \[ 113.04 \times \frac{5}{12} \approx 113.04 \times 0.4167 \approx 47.1 \text{ square inches} \]
Thus, the area of the pizza that was eaten is approximately 47.1 square inches.
Therefore, the answer is: 47.1 square inches.