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The problem describes a quarter circle with a radius of 12 cm, and asks for the perimeter of the shape in exact form.

### Perimeter of a quarter circle:
The perimeter consists of:
1. The curved part (which is a quarter of the circumference of the full circle).
2. Two straight lines, which are the radii of the quarter circle.

1. **Curved part of the perimeter**:
   - The circumference of a full circle is given by \( 2\pi r \), where \( r \) is the radius.
   - Since this is a quarter circle, the curved length is \( \frac{1}{4} \times 2\pi r = \frac{1}{4} \times 2\pi \times 12 = 6\pi \, \text{cm} \).

2. **Straight parts (radii)**:
   - There are two straight parts, each equal to the radius. So, the total length of the straight parts is \( 12 + 12 = 24 \, \text{cm} \).

### Total Perimeter:
The total perimeter is the sum of the curved part and the two straight parts:
\[
\text{Perimeter} = 6\pi + 24 \, \text{cm}
\]

Thus, the exact form of the perimeter is:
\[
\boxed{6\pi + 24 \, \text{cm}}
\]

Would you like further clarification or details? Here are five related questions you could explore:

1. How do you calculate the area of a quarter circle?
2. What is the perimeter of a semicircle with a radius of 12 cm?
3. How would the perimeter change if the radius of the quarter circle were doubled?
4. What is the formula for the arc length of any circle sector?
5. How do you express the perimeter of the quarter circle in decimal form?

**Tip**: Always remember to consider both the curved and straight parts when calculating the perimeter of a sector or part of a circle.

The diagram shows a quarter circle of radius 12cm. Find the perimeter of the shape, give your answer in exact form.

Learn how to calculate the perimeter of a quarter circle with radius 12 cm. This geometry problem involves calculating both the arc length and the straight sides of the shape. Suitable for students in Grades 8-10.

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