Final answer:
The area of the triangular garden is calculated using the formula A = ½ × base × height with the given measurements. After converting the base and height to improper fractions, the area is found to be 7.5 square feet, which does not match any of the provided options.
Step-by-step explanation:
To find the area of a triangular garden, we use the formula for the area of a triangle, A = ½ × base × height. In this case, the base is given as 4 1/2 feet and the height as 6 2/3 feet.
Firstly, we convert these mixed numbers to improper fractions:
Base: 4 1/2 = (4 × 2 + 1) / 2 = 9/2 feetHeight: 6 2/3 = (6 × 3 + 2) / 3 = 20/3 feet
Now, we substitute these values into the area formula:
A = ½ × (9/2) × (20/3) = (1/2) × (9 × 20) / (2 × 3) = (1/2) × 90/6 = 45/6 = 7.5 square feet
Therefore, none of the multiple-choice options given (A, B, C, D) are correct. The area of the garden is 7.5 square feet.