Calculate Arc Length Here we are going to learn about Arc length and formula to find the Arc Length. Arc Length is nothing but length or an arc. Arc is a curve. We can also call it as arc length of a curve. Arc length is defined as the measure of the distance along the curved line making up an arc. The arc length is longer than the straight line distance between its end points. We can consider an segment in a circle, which is an arc. Consider the below figure In the figure shown above, the arc length is the blue coloured portion indicated by s. Let be the angle made by the end points with the center of the circle. The distance from one end point of the curve or arc to the center is called as radius. If we know the radius and value we can find out the arc length using the below formula. Arc Length Practice Problems Problem 1: Evaluate the arc length of a circle of diameter and the central angle 1800. Know More About Area of a Triangle Worksheet
Answer : The arc length of the circle which is the semicircular arc is Problem 2: Evaluate the arc length of a circle of radius 9 cm and the central angle 1200 Answer : The arc length of the circle is 18.84 cm Example 2: Calculate the arc length of a circle with circumference 31.42 cm and the the central angle is given by 450 . Solution : Step 1: As the circumference of the circle is given, the radius of the circle can be calculated as mentioned in the above formula table.
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12 Sided Polygon Dodecagon is one of the types of polygon which has 12 sides. This is one of the regular polygons and is named dodecagon since it has 12 sides. Dodecagon has 12 angles. There are both regular and irregular dodecagons. Here, we will discuss more about the properties of the regular 12 sided polygon. Area of a Dodecagon The total space inside the boundary of the Dodecagon is called as the area of a Dodecagon.The area of a Dodecagon of side length d is given by, Area = 3(2 + âˆš3)d2. The area calculated using the radius R of the circumscribed circle is, Area = 3R2. Properties of a Dodecagon
The total interior angle of a 12 sided polygon is = (12 - 2) 180 degrees = 1800 degrees. The internal angle at each vertex is equal to = 180012 = 150 degrees. The total exterior angle of a 12 sided polygon is 360 degrees. While the exterior angle at a single vertex is = 36012 = 30 degrees. The number of all possible diagonals in a 12 sided polygon is given by the formula, Total diagonals = n(n - 3)/2 = 12(12 - 3)/2 = 6x9 = 54. So, the number of all possible diagonals in a 12 sided polygon is equal to 54. The number of triangles formed by the diagonals from each vertex of a 12 sided polygon is, Triangles formed = n - 2 = 12 - 2 = 10. How to Find the Area of a Dodecagon Given below are some of the examples on dodecagon Example 1: Calculate the area of the 12 sided polygon with side length d= 5 cm. Read More About Permutations and Combinations Worksheet
Solution: Area of 12 sided polygon = 3(2+√3)d2. = 3(2+√3) x52 = 3(2+√3) x 25 = 75(2+√3) = 279.90 cm2.