To find the area of A’Leila's pen for her pet donkey, we first need to understand the relationship between the two sides of the rectangle. A’Leila has defined the sides \( a \) and \( b \) such that:
\[ a = \frac{1}{3} b \]
Step 1: Express the area in terms of \( b \)
The area \( A \) of a rectangle is given by the formula:
\[ A = a \times b \]
Substituting \( a \) from the given relationship:
\[ A = \left(\frac{1}{3} b\right) \times b \]
Step 2: Simplify the expression
Now, simplify the expression:
\[ A = \frac{1}{3} b^2 \]
Conclusion
Thus, the area of A’Leila's pen in terms of \( b \) is:
\[ A = \frac{1}{3} b^2 \]
If A’Leila knows the value of \( b \), she can plug that value into this formula to find the area of the pen.