Final answer:
To find the area of the rectangle with sides 5 1/6 and 2 2/7 feet, convert the mixed numbers to improper fractions, multiply them, and simplify. The area is 11 17/21 square feet.
Step-by-step explanation:
To work out the area of the rectangle using its given dimensions 5 1/6 feet and 2 2/7 feet, you must first convert these mixed numbers to improper fractions.
For 5 1/6, multiply 5 by 6 and add 1 to get an improper fraction of 31/6. For 2 2/7, multiply 2 by 7 and add 2 to obtain an improper fraction of 16/7.
Now, to find the area of the rectangle, multiply the two improper fractions:
Area = (31/6) × (16/7) = (31 × 16) / (6 × 7)
Simplify the multiplication to get Area = 496 / 42. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2:
Area = 248 / 21
Now, convert this improper fraction back to a mixed number by dividing 248 by 21:
11 remainder 17, so the area is 11 17/21 square feet.