Final answer:
The area of a rectangle with side lengths of 3/4 yard and 5/6 yard is calculated by multiplying the lengths of the sides, resulting in an area of 5/8 square yards.
Step-by-step explanation:
To find the area of a rectangle, you multiply the length of one side by the length of the adjacent side. In the case of a rectangle with side lengths of 3/4 yard and 5/6 yard, you would calculate the area as follows:
Area = length × width
Area = (3/4 yard) × (5/6 yard)
To multiply these fractions, multiply the numerators together and the denominators together:
Area = (3 × 5) / (4 × 6)
Area = 15 / 24
Next, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 3:
Area = (15 ÷ 3) / (24 ÷ 3)
Area = 5 / 8
Therefore, the area of the rectangle is 5/8 square yards.