Respuesta :
The area of sector ABC is 14.24 units.
The area of sector of a circle is the amount of space enclosed within the boundary of the sector. A sector always originates from the center of the circle. The sector of a circle is defined as the portion of a circle that is enclosed between its two radii and the arc adjoining them. The semi-circle is the most common sector of a circle, which represents half a circle. The space enclosed by the sector of a circle is called the area of the sector. There are two types of sectors: minor and major sectors. A minor sector is a sector that is less than a semi-circle, whereas, a major sector is a sector greater than a semi-circle.
m∠ABC = θ = 102°
Radius of circle = AB = r = 4 units
Area of sector of a circle
Area = (θ/360°) × πr²
Substitute the above values in the formula:
Area = (102/360) × π ×4²
= 14.24188 square units
Rounding off to the nearest hundredth decimal,
Area = 14.24 square units
Thus, the area of sector ABC is 14.24 units.
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