Final answer:
To find the area of Nikki's rectangular backyard, the width must first be calculated using the expression (1/3) × length + 4 feet, which equates to 13 feet. Then, the area is found by multiplying the length (27 feet) by the width (13 feet), resulting in an area of 351 square feet.
Step-by-step explanation:
Nikki's backyard is the shape of a rectangle, and the task is to write and evaluate an expression to find the area of her backyard. Since the area of a rectangle is found by multiplying the length by the width, we first need to determine the width of Nikki's backyard. We are told that the width is one-third of the length plus 4 feet. The length is given as 27 feet.
The width can be expressed as (1/3) × 27 feet + 4 feet. Now, we calculate the width:
Width = (1/3) × 27 feet + 4 feet = 9 feet + 4 feet = 13 feet.
With both dimensions known, we can find the area of the backyard (Area = length × width):
Area = 27 feet × 13 feet = 351 square feet.
Therefore, the area of Nikki's backyard is 351 square feet.