Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Since the area of a circle is directly proportional to the square of the radius, their ratio should be maintained for different proportions, therefore, we have the following relation
[tex]\frac{50.24}{4^2}=\frac{A}{6^2}[/tex]
Where A represents the area of a circle with radius 6 ft. Solving for A, we have
[tex]\begin{gathered} \frac{50.24}{4^2}=\frac{A}{6^2} \\ \frac{50.24}{16}=\frac{A}{36} \\ A=\frac{50.24}{16}\cdot36 \\ A=113.04 \end{gathered}[/tex]
The area is 113.04 ft².
