To find the area of the composite figure in terms of $\pi$, we need to divide it into simpler shapes and calculate the area of each.

Breakdown of the Composite Figure:

• Rectangular section: A rectangle with dimensions 5 cm by 5 cm.
• Quarter circle section: A quarter of a circle with a radius of 3 cm.

Step 1: Area of the Rectangle

The area $A_{\text{rect}}$ of the rectangle is given by: $A_{\text{rect}} = \text{length} \times \text{width} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2$

Step 2: Area of the Quarter Circle

The area $A_{\text{quarter circle}}$ of a full circle is $\pi r^2$, and since we have a quarter of a circle, the area is: $A_{\text{quarter circle}} = \frac{1}{4} \times \pi r^2 = \frac{1}{4} \times \pi \times (3 \, \text{cm})^2 = \frac{1}{4} \times \pi \times 9 = \frac{9\pi}{4} \, \text{cm}^2$

Step 3: Total Area

Now, sum the areas of the rectangle and the quarter circle: $A_{\text{total}} = A_{\text{rect}} + A_{\text{quarter circle}} = 25 \, \text{cm}^2 + \frac{9\pi}{4} \, \text{cm}^2$

Thus, the total area of the composite figure is: $A_{\text{total}} = 25 + \frac{9\pi}{4} \, \text{cm}^2$

This is the area of the composite figure in terms of $\pi$.

Do you want more details, or have any questions?

Here are some related questions to explore:

1. How would the area change if the radius of the quarter circle increased to 4 cm?
2. How do you calculate the perimeter of the composite figure?
3. What would be the area if the shape had a semicircle instead of a quarter circle?
4. How do composite figures help in solving real-world geometry problems?
5. How would the formula change if the rectangle's dimensions were different?

Tip: Always break down complex shapes into simpler ones to calculate areas or other properties more easily.