To find the area of the sector that is not shaded, we first need to understand the context of the problem, which presumably involves a circle and some shaded portion of it.
Let’s say you have a circle and it’s divided into sectors. To find the area of the complete sector, you would typically use the formula:
Area of the sector = (θ / 360) * π * r²
Where:
- θ is the central angle of the sector in degrees.
- r is the radius of the circle.
If we are given specific angles and areas, we must determine the area of the entire circle and subtract the area of the shaded sector. Assuming you have a sector defined by the angles mentioned (e.g., 12°, 24°, 120°, and 144°), you will need to sum the angles of the shaded sectors.
For instance, if you had a shaded sector of 120° and 144°, you calculate:
Area of shaded sector = [(120 + 144) / 360] * π * r²Once you have that area, the area of the non-shaded portion can be calculated by:
Area of non-shaded sector = Area of circle - Area of shaded sectorTo summarize:
- Determine the radius of the circle, if not provided.
- Calculate the area of the full circle (using r).
- Find the area of the shaded sector with the provided angles.
- Subtract the shaded area from the total circle area to get the non-shaded area.