Question

the radius of the circle is 4 cm and the measure of the central angle is 90°. the area of the sector with a central angle measuring 90° and radius of length 4 cm is dropdownπ cm². the triangle in the sector is dropdown. the area of the triangle is dropdowncm². the area of the segment of the circle is (4π − dropdown) cm².

Explanation:

Answer:

The area of the sector: \( 4 \)
The triangle in the sector: isosceles right triangle
The area of the triangle: \( 8 \)
The area of the segment: \( 8 \)

(Explanation for each part:

1. Area of sector: \( \frac{\theta}{360^\circ} \times \pi r^2 = \frac{90^\circ}{360^\circ} \times \pi \times 4^2 = 4\pi \), so the coefficient of \( \pi \) is \( 4 \).
2. The triangle has two sides equal to the radius (4 cm each) and a right angle, so it's an isosceles right triangle.
3. Area of triangle: \( \frac{1}{2} \times 4 \times 4 = 8 \) \( \text{cm}^2 \).
4. Area of segment = Area of sector - Area of triangle = \( 4\pi - 8 \), so the missing value is \( 8 \).)