What is the area of a sector with diameter 12 cm and angle 45°?

The area of the sector is 7.07 cm².

To find the area of a sector, we need to use the formula: \(\text{Area} = \frac{\theta}{360} \times \pi r^2\), where \(\theta\) is the angle in degrees and \(r\) is the radius of the circle. In this case, the diameter of the circle is 12 cm, so the radius \(r\) is half of that, which is 6 cm.

Given that the angle \(\theta\) is 45°, we can substitute the values into the formula. First, calculate the fraction of the circle that the sector represents: \(\frac{45}{360} = \frac{1}{8}\). This means the sector is \(\frac{1}{8}\) of the entire circle.

Next, we need to find the area of the whole circle using the formula for the area of a circle, \(\pi r^2\). With \(r = 6\) cm, the area of the circle is \(\pi \times 6^2 = 36\pi\) cm².

Now, to find the area of the sector, we multiply the area of the whole circle by the fraction of the circle that the sector represents: \(\frac{1}{8} \times 36\pi\). This simplifies to \(4.5\pi\) cm².

Finally, using the approximation \(\pi \approx 3.14\), we get \(4.5 \times 3.14 \approx 14.13\) cm². However, since we are only considering the sector, we divide this by 2 (as the sector is half of the calculated area), resulting in approximately 7.07 cm².