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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.

Find the area of the composite figure in terms of π.

Learn how to calculate the area of a composite figure that consists of a rectangle and a quarter circle. The rectangle has dimensions of 5 cm by 5 cm, while the quarter circle has a radius of 3 cm. Find the total area in terms of π, suitable for students in Grades 6-8.

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