Perimeter of Arc

The perimeter of an arc is the length of the curved boundary of a part of a circle. It is calculated as a fraction of the circumference of the circle, which is proportional to the angle that the arc subtends at the center of the circle. The formula for the perimeter of an arc is 𝑃 = 2πr(θ/360) + 2r, where r is the radius of the circle and θ is the angle in degrees. For instance, if a circle has a radius of 5 units and the arc subtends an angle of 60 degrees, then its perimeter is 𝑃 = 2π(5)(60/360) + 2(5) = 5π/3 + 10.

Let’s consider another example of calculating the perimeter of an arc with a circle of radius 7 units and an angle of 90 degrees. The perimeter of the arc will be: 𝑃 = 2π(7)(90/360) + 2(7) = 7π/2 + 14.

To find the perimeter of an arc, apply the given formula and calculate both the arc length and the two radii. For instance, if a circle has a radius of 8 units and the arc subtends an angle of 45 degrees, then: Arc Length = 2π(8)(45/360) = π/2 Perimeter = Arc Length + 2(8) = π/2 + 16 units. Example Problem on Perimeter of Arc - For finding the perimeter of an arc, we use the formula, 𝑷 = 2πr(θ/360) + 2r. For example, let’s say, r = 6 units and θ = 120 degrees. Now, the perimeter = Arc Length + 2r = 2π(6)(120/360) + 2(6) = 4π + 12. Therefore, the perimeter of the arc is 4π + 12 units.

Learning some tips and tricks makes it easier for children to calculate the perimeter of arcs. Here are some tips and tricks given below: Always remember that an arc's perimeter involves both the arc length and the two radii of the circle. Use the formula, 𝑷 = 2πr(θ/360) + 2r. Calculating the arc length starts by determining the radius and the angle. Ensure the angle is in degrees for using the formula. To reduce confusion, arrange the given measurements clearly when dealing with multiple arcs. Apply the formula to each arc separately. To avoid mistakes when calculating the perimeter, ensure the radius and angle measurements are accurate and consistent, especially for practical uses like construction and decoration. If you are given the arc length and need to find the perimeter, remember to add twice the radius to the arc length.

Arc: A part of the circumference of a circle. Radius: The distance from the center of a circle to any point on its boundary. Angle: The measure in degrees of the circle's sector that the arc spans. Circumference: The total length around a circle. Perimeter of Arc: The sum of the arc length and twice the radius.