Perimeter of Segment

The perimeter of a segment is the total length along the arc and the two radii. By adding the arc length and the lengths of both radii, we get the perimeter of the segment. The formula for the perimeter of a segment is 𝑃 = 𝑟𝜃 + 2𝑟, where 𝑟 is the radius and 𝜃 is the angle (in radians) subtended by the arc at the center of the circle. For instance, if a segment has a radius 𝑟 = 6 and an angle 𝜃 = 1 radian, then its perimeter is 𝑃 = 6 × 1 + 2 × 6 = 18.

Let’s consider another example of a segment with a radius 𝑟 = 8 and an angle 𝜃 = 1.5 radians. So the perimeter of the segment will be: 𝑃 = 𝑟𝜃 + 2𝑟 = 8 × 1.5 + 2 × 8 = 28.

To find the perimeter of a segment, we just need to apply the given formula and sum the arc length and the lengths of the radii. For instance, a given segment has a radius 𝑟 = 6 and an angle 𝜃 = 2 radians. Perimeter = arc length + sum of radii = 6 × 2 + 2 × 6 = 24 cm. Example Problem on Perimeter of Segment - For finding the perimeter of a segment, we use the formula, 𝑃 = 𝑟𝜃 + 2𝑟. For example, let’s say, 𝑟 = 5 cm and 𝜃 = 1.2 radians. Now, the perimeter = arc length + sum of radii = 5 × 1.2 + 2 × 5 = 16 cm. Therefore, the perimeter of the segment is 16 cm.

Learning some tips and tricks makes it easier for children to calculate the perimeter of segments. Here are some tips and tricks given below: Always remember that a segment's perimeter is the sum of the arc length and the two radii. For that, use the formula, 𝑃 = 𝑟𝜃 + 2𝑟. Calculating the perimeter of a segment starts by determining the arc length using the angle in radians. The formula for the arc length is: Arc Length = 𝑟𝜃. To reduce confusion, specifically arrange the given measurements if you need the perimeter of a group of segments. After that, apply the formula to each segment. To avoid mistakes when adding the perimeter, make sure the measurements are precise and constant for common uses like landscaping and architecture. If you are given the central angle in degrees, convert it to radians before calculating the arc length using the formula: Radians = Degrees × (π/180).

Perimeter: The total length around a shape, including all its sides or edges. Segment: A part of a circle bounded by an arc and the radii joining the endpoints of the arc to the center. Arc Length: The distance along the curved line making up the arc, calculated as 𝑟𝜃. Radius: A straight line from the center of a circle to any point on its circumference. Central Angle: The angle subtended at the center of a circle by two radii.