https://file.aiquickdraw.com/mathbot/file/1725951006945vhfqegaq.jpg

The problem asks to determine the area of the shaded region in a circle. Given the image:

- The circle has a radius \( r = 14 \) cm.
- \( \angle AOB \) is a right angle, which means it is \( 90^\circ \).

### Steps to solve:

1. **Calculate the area of the sector \( AOB \):**

   The area of a sector is given by:
   \[
   \text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
   \]
   Here, \( \theta = 90^\circ \) and \( r = 14 \) cm.
   \[
   \text{Area of sector} = \frac{90^\circ}{360^\circ} \times \pi \times 14^2 = \frac{1}{4} \times \pi \times 196 \text{ cm}^2 = 49\pi \text{ cm}^2
   \]

2. **Calculate the area of triangle \( OAB \):**

   Since \( \triangle OAB \) is a right triangle with both legs as the radii of the circle:
   \[
   \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 14 \times 14 = 98 \text{ cm}^2
   \]

3. **Determine the area of the shaded region:**

   The shaded region is the area of the sector minus the area of the triangle:
   \[
   \text{Area of shaded region} = 49\pi \text{ cm}^2 - 98 \text{ cm}^2
   \]

### Approximate Numerical Value:
To give a numerical approximation, use \( \pi \approx 3.14 \):
\[
\text{Area of shaded region} = 49 \times 3.14 - 98 = 153.86 \text{ cm}^2 - 98 \text{ cm}^2 = 55.86 \text{ cm}^2
\]

### Final Answer:
The area of the shaded region is approximately **55.86 cm²**.

Would you like any further details or clarifications?

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**Related Questions:**

1. How would the result change if the radius were doubled?
2. What is the general formula for the area of a shaded region for any given central angle \( \theta \)?
3. How does the area of the shaded region compare if \( \theta \) is 180° instead of 90°?
4. What is the circumference of the circle in this problem?
5. How would you calculate the perimeter of the shaded region?

**Tip:** Remember to always check the angle measure and ensure it's correctly applied in sector area calculations.

Tentukan luas daerah yang diarsir pada gambar lingkaran dengan jari-jari 14 cm dan sudut pusat 90°.

Find the shaded area in a circle with a radius of 14 cm and a 90° central angle by using sector and triangle area formulas. Learn step-by-step calculations including the subtraction of triangle area from the sector area. Suitable for Grades 10-12.

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