Final answer:
To find the area of the rectangle, multiply the length and width after converting the mixed numbers to improper fractions. The area is 35 1/4 square meters.
Step-by-step explanation:
To find the area of a rectangle, you multiply its length and width. In this case, the length is 4 2/4 meters and the width is 7 5/6 meters. To multiply mixed numbers, convert them into improper fractions. The length becomes 18/4 and the width becomes 47/6. Now multiply the fractions together: (18/4) * (47/6) = 846/24. Simplifying the fraction gives us 35 1/4. Therefore, the area of the rectangle is 35 1/4 square meters.