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How do you find the arc length of a circle that has an inscribed polygon?
Wiki User
∙ 6y ago
What do you mean by "arc length of a circle"?
If you mean the arc length between two adjacent vertices of the inscribed polygon, then:
If the polygon is irregular then the arc length between adjacent vertices of the polygon will vary and it is impossible to calculate and the angle between the radii must be measured from the diagram using a protractor if the angle is not marked. The angle is a fraction of a whole turn (which is 360° or 2π radians) which can be multiplied by the circumference of the circle to find the arc length between the radii:
arc_length = 2πradius × angle/angle_of_full_turn
→ arc_length = 2πradius × angle_in_degrees/360°
or arc_length = 2πradius × angle_in_radians/2π = radius × angle_in_radians
If there is a regular polygon inscribed in a circle, then there will be a constant angle between the radii of the circle between the adjacent vertices of the polygon and each arc between adjacent vertices will be the same length; assuming you know the radius of the circle, the arc length is thus one number_of_sides_th of the circumference of the circle, namely:
arc_length_between_adjacent_vertices_of_inscribed_regular_polygon = 2πradius ÷ number_of_sides
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoAny circle can have lots of different kinds of inscribed polygons and there is no relationship between the number of sides in the polygon and an arc length.
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How do you find out if the polygon of a circle is regular or not?
I assume you mean a polygon inscribed in a circle. It is regular if all its sides and angles are equal.
What are the measures in a regular polygon?
The area of a regular polygon is given by the following formula: area =(1/2) (apothem)(perimeter).There are several other formulas that can be used. Regular Polygon Formulas are: N=number of sides, s= length, r = apothem (adiius of inscribed circle) R = radius of circumcircle. Using any of these formulas you can find the measurements of a regular polygon.
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
How do you find the area of a hexagon that is inscribed in a circle?
The area of any hexagon is 6(0.5)(L)(L sin 60o) = 3L2 sin 60o, where L is the length of one side and is also the radius of the circumscribed circle.
A circle is inscribed in an equilateral triangle of side 6 find area of square inscribed in a circle?
The answer in 6.... draw an angular bisector from one of the angles to the centre of circle then draw a perpendicular from the centre of circle. Those to lines will form a triangle... use trigonometry and find the length of the perpendicular, which is also a radius... double the radius and u will get the diagonal for the square... using formula :- (Side)^2 + (Side)^2 = (Diagonal)^2, find the side of square and square the answer, which will give you your final answer
How do you find out if the polygon of a circle is regular or not?
I assume you mean a polygon inscribed in a circle. It is regular if all its sides and angles are equal.
What are the measures in a regular polygon?
The area of a regular polygon is given by the following formula: area =(1/2) (apothem)(perimeter).There are several other formulas that can be used. Regular Polygon Formulas are: N=number of sides, s= length, r = apothem (adiius of inscribed circle) R = radius of circumcircle. Using any of these formulas you can find the measurements of a regular polygon.
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
How do you find the circumference of a circle inscribed in a rhombus?
To find the circumference of a circle in rhombus you eat SH*t .
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming?
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a in C programming
Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius a?
The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.
Is there a regular polygon with an interior angle sum 9000?
A polygon with n sides inscribed in a circle has an angle sum of 180xn-360 So the problem is find n so that 180n-360=9000 => n=48 The regular polygon with an angle sum of 9000 has 48 sides
How do you find the radius of a square?
A square does not have a radius. A square, with sides of length x units, can have an inscribed circle. Such a circle would have a radius of x/2 units. Or the square could have a circumscribing circle. This would have a radius of x/sqrt(2) units.
How do you find the area of a hexagon that is inscribed in a circle?
The area of any hexagon is 6(0.5)(L)(L sin 60o) = 3L2 sin 60o, where L is the length of one side and is also the radius of the circumscribed circle.
A circle is inscribed in an equilateral triangle of side 6 find area of square inscribed in a circle?
The answer in 6.... draw an angular bisector from one of the angles to the centre of circle then draw a perpendicular from the centre of circle. Those to lines will form a triangle... use trigonometry and find the length of the perpendicular, which is also a radius... double the radius and u will get the diagonal for the square... using formula :- (Side)^2 + (Side)^2 = (Diagonal)^2, find the side of square and square the answer, which will give you your final answer
How do you find the area of a triangle with a inscribed circle outside the circle?
usually: 1/2 b x h
How do you find the permeter of a polygon?
The perimeter of a polygon is the sum of the length of each of its sides. If the polygon is a regular polygon the you can calculate the perimeter as [number of sides] *[the length of one side]
