Question

question 7 of 10

if the area of the circle below is \\(12\text{ m}^2\\), what is the area of the shaded sector?

a. \\(3\text{ m}^2\\)
b. \\(4\text{ m}^2\\)
c. \\(6\text{ m}^2\\)
d. \\(2\text{ m}^2\\)

Explanation:

Identify the given values

Using the Area of a Sector knowledge point

$$
LATEXBLOCK0
$$

Calculate the sector area fraction

Using the Area of a Sector knowledge point

$$ \text{Fraction} = \frac{\theta}{360^\circ} = \frac{90^\circ}{360^\circ} = \frac{1}{4} $$

Compute the area of the shaded sector

Using the Area of a Sector knowledge point

$$ A_{\text{sector}} = \text{Fraction} \times A_{\text{circle}} = \frac{1}{4} \times 12\text{ m}^2 = 3\text{ m}^2 $$

Answer:

• (A) \(3\text{ m}^2\) (Correct answer)
• (B) \(4\text{ m}^2\)
• (C) \(6\text{ m}^2\)
• (D) \(2\text{ m}^2\)