Explanation:

To find the area of the sector, use the formula:

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

Where:

- $\theta$ is the central angle in degrees.

- $r$ is the radius of the circle.

Plug the values into the formula:

- $\theta ={90}^{\circ }$

- $r=7\text{cm}$

$$\text{Area of sector}=\frac{90}{360}\times \pi \times 7^2$$

$$=\frac{1}{4}\times \pi \times 49$$

$$\approx \frac{1}{4}\times 3.1416\times 49$$

$$\approx 38.48{\text{cm}}^2$$

- Option 1: 38.50 cm² – This is the closest value.

- Option 2: 35 cm² – This is less than calculated.

- Option 3: 20.67 cm² – This is much too low.

- Option 4: 28 cm² – Also too low.

Thus, the correct answer aligns with Option 1: 38.50 cm².

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