Final answer:
The area of the rectangular playground is 42 square meters.
Step-by-step explanation:
To find the area of a rectangular playground, we need to use the formula: Area = length x width. In this case, we are given one side of the playground as 6 meters long. To find the other side, we can use the formula for the perimeter of a rectangle: Perimeter = 2(length + width). Since the perimeter is given as 26 meters, we can substitute the given values and solve for width: 26 = 2(6 + width). Solving this equation, we find that the width is 7 meters.
Now, we have the length as 6 meters and the width as 7 meters. We can substitute these values into the formula for area: Area = length x width. Thus, the area of the playground is 6 x 7 = 42 square meters.