Final answer:
To approximate the area of the paved lunch region consisting of a semi-circle and a trapezoid, the formula for the area of a trapezoid and a semi-circle were used. The calculations suggest that none of the provided options are correct given the specified dimensions. There may be missing details or errors in the question.
Step-by-step explanation:
The subject of this question is to find the area of the paved lunch region which includes a semi-circle and a trapezoid. To calculate the area of the trapezoid, we use the formula: A = ½ × (base1 + base2) × height. The semi-circle's area is ½ × π × r², where the radius (r) is half of the diameter. The diameter of the semi-circle is given as the same as base1, which is 8 feet, so the radius is 4 feet.
First, calculate the area of the trapezoid:
A = ½ × (8ft + 16ft) × 8ft = ½ × 24ft × 8ft = 96ft².
Then, calculate the area of the semi-circle:
A = ½ × π × (4ft)² = 2× π × 4² = 2× π × 16 = 32π ≈ 32 × 3.14 ≈ 100.48ft².
Add both areas to get the total area:
96ft² + 100.48ft² ≈ 196.48ft².
This approximation does not correspond exactly to the provided answers, which suggests there may be some missing information or an error in the provided dimensions. However, with the given information, none of the provided answers are correct.