Final answer:
The area of the rectangle is calculated by finding the not-given side's measurement using the perimeter and then multiplying the length by the width, resulting in an area of 54 square feet.
Step-by-step explanation:
If the perimeter of a rectangle is 30 feet and one side is 6 feet long, we need to find the length of the other side to calculate the area of the rectangle.
The perimeter of a rectangle is the sum of all sides, which can be represented as P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Given that one side (width) is 6 feet, and the perimeter is 30 feet, we can set up the equation:
30 = 2l + 2(6)
30 = 2l + 12
18 = 2l
l = 9 feet
Now that we know both the length and the width, we can find the area of the rectangle by multiplying the length by the width:
Area = l × w
Area = 9 × 6
Area = 54 square feet
Therefore, the area of the rectangle is 54 square feet.