Table of Contents
How do you find the dimensions of an octagon?
Multiply the diameter’s length, the distance from vertex to opposite vertex, by 0.383 to calculate a side’s length. For example, the diameter is 10 inches — 10 inches multiplied by 0.383 results in 3.83 inches.
What is the perimeter of a regular octagon inscribed in circle?
8b
The perimeter of the octagon is 8b since it has been divided into eight congruent triangles each with a base of b. We can calculate the angles of these eight triangles using the fact that the eight inner angles combine to make a 360 degree circle so each measures 45 degrees.
How do you find the radius of an inscribed octagon?
- Side of the regular octagon =a.
- Angle subtended by the side=360⁰/8=45⁰
- The radius “R” of the inscribed circle is the altitude from the center to the side.
- Hence (a/2)/R=tan (45⁰/2)
- Hence R=a/(2tan22.5⁰)=0.818a.
- Hence area =π(0.818a)²= 2.156a²
What is the area of an octagon with a radius of 8?
The area of each of the 8 congruent triangles described above is computed as about 22.6273 sq cm. This leads to octagonal area is 181.02 sq cm.
What is the area of a regular octagon inscribed in a circle of radius r?
So, the correct answer is “ =2√2r2 ”.
How do you find the area of a regular polygon with the apothem?
You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.
How do you find the diameter of an inscribed octagon?
By the symmetry a line segment from the centre of the circle to the midpoint of a side of the octagon is a radius of the circle. Hence the diameter of the inscribed circle is the width of octagon. If you know the side lengths of a regular octagon then the diameter can be found using the method that I used in the answer to a previous question.
How to construct a regular octagon from a circle?
Construct a regular octagon given the perpendicular distance from one side of the octagon to the opposite (i.e. twice the radius of the inscribedcircle). Build a square around the circle and construct the octagon from that. 5. What is the length of the Apothemof a regular octagon with side of length a.
What is the use of octoctagon formula?
Octagon formula helps us to compute the area and perimeter of octagonal objects. Consider a regular octagon with each side “ a” units. Area of an octagon is defined as the region occupied inside the boundary of an octagon.
What is the formula for the perimeter of an octagon?
Perimeter of an octagon is defined as the length of the boundary of the octagon. So perimeter will be the sum of the length of all sides. The formula for perimeter of an octagon is given by: It has eight sides and eight angles.