To find the area of a sector of a circle, you can use the following formula:

$\text{Area of the sector} = \frac{\theta}{360^\circ} \times \pi r^2$

Given:

• $r = 10.3 \, \text{cm}$
• $\theta = 69^\circ$

Substitute the values into the formula:

$\text{Area} = \frac{69^\circ}{360^\circ} \times \pi \times (10.3 \, \text{cm})^2$

Now, let's calculate it:

$\text{Area} = \frac{69}{360} \times \pi \times 10.3^2$

$\text{Area} = \frac{69}{360} \times \pi \times 106.09 \, \text{cm}^2$

$\text{Area} \approx 0.1917 \times 3.1416 \times 106.09 \, \text{cm}^2$

$\text{Area} \approx 63.83 \, \text{cm}^2$

So, the area of the sector is approximately 63.83 cm².

Would you like more details or have any questions? Here are some related questions:

1. What would the area of the sector be if the radius was 15 cm?
2. How does changing the central angle to 90° affect the area of the sector?
3. What is the total area of the circle if the radius is 10.3 cm?
4. How does the area of the sector compare to the total area of the circle?
5. What would the area be if the angle were given in radians instead of degrees?

Tip: When working with sector area problems, remember that the area is directly proportional to both the square of the radius and the central angle.