Question

1. what is the area of major sector dfe?

8.7 cm
260°
158.49 square cm
207.60 square cm
171.69 square cm
199.89 square cm

Explanation:

Step1: Recall sector area formula

The area of a sector is given by $\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2$, where $\theta$ is the central angle of the sector, and $r$ is the radius of the circle.

Step2: Identify given values

Here, $\theta = 260^\circ$, $r = 8.7$ cm.

Step3: Substitute values into formula

$$ \text{Area} = \frac{260^\circ}{360^\circ} \times \pi \times (8.7)^2 $$

First calculate $(8.7)^2 = 75.69$. Then simplify $\frac{260}{360} = \frac{13}{18}$.

$$ \text{Area} = \frac{13}{18} \times \pi \times 75.69 $$

Step4: Compute the numerical value

Calculate $\frac{13 \times 75.69}{18} = \frac{983.97}{18} \approx 54.665$. Then multiply by $\pi \approx 3.1416$:
$54.665 \times 3.1416 \approx 171.69$

Answer:

171.69 square cm