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What is an Apothem in math give the definition of it?
The apothem, for a circle, is the perpendicular distance from a chord to the centre of the circle.
How is an apothem different from a radius?
An apothem is a line drawn perpendicular to a side of a regular polygon from the center of the polygon. A polygon is not a circle so it cannot have a radius. The radius of a circle is drawn from the center to any point in the circumference of the circle. You can draw a circle which encloses the regular polygon touching all vertices. The polygon is said to be inscribed in the circle. The apothem will be less than the radius because the radius is not perpendicular to any side, it can be drawn to a vertex but the apothem is perpendicular to a side, so it is shorter. Ex: draw a square with a circle which inscribes it. You can see that the apothem will be less than the radius.
What is the perimeter of a hexagon having 225 cm square area of a circle inscribed in it?
Area of circle = 225 cm2 implies radius = 8.46 cm (approx) Therefore, apothem of hexagon = 8.46 cm then side of hexagon = apothem*2/sqrt(3) = 9.77 cm (approx) and so perimeter = 6*side = 58.63 cm
What is the perimeter of a hexagon with an apothem of 12?
The perimeter of a hexagon with an apothem of 12 is 83.14
How do you find the apothem of an octagon with the diameter?
You can only do this for a regular octagon. It is much easier to understand the method if you do a rough sketch and follow the explanation using that. Unfortunately, this browser does not support any kind of drawing! Suppose the diameter of the octagon is D. Therefore the diameter of the circumscribing circle is also D. Form the centre of this circle, draw lines to two adjacent vertices of the octagon. The lengths of these lines is D/2 because these are radii of the circle. These lines and the side of the octagon form an isosceles triangle, and the apothem is the height of this triangle. Now consider half this triangle: the right angled triangle formed by the apothem, half the side of the octagon and the radius. The angles at the apex of the octagon is 360/8 = 45 degrees. So the angle at the apex of the right angled triangle is half that = 22.5 degrees. Then cos(22.5 deg) = Apothem/Radius So that Apothem = Radius*cos(22.5 deg) = D/2*0.9239 (approx).
What is an Apothem in math give the definition of it?
The apothem, for a circle, is the perpendicular distance from a chord to the centre of the circle.
Can a circle have an apothem?
yes
How is an apothem different from a radius?
An apothem is a line drawn perpendicular to a side of a regular polygon from the center of the polygon. A polygon is not a circle so it cannot have a radius. The radius of a circle is drawn from the center to any point in the circumference of the circle. You can draw a circle which encloses the regular polygon touching all vertices. The polygon is said to be inscribed in the circle. The apothem will be less than the radius because the radius is not perpendicular to any side, it can be drawn to a vertex but the apothem is perpendicular to a side, so it is shorter. Ex: draw a square with a circle which inscribes it. You can see that the apothem will be less than the radius.
What is the perimeter of a hexagon having 225 cm square area of a circle inscribed in it?
Area of circle = 225 cm2 implies radius = 8.46 cm (approx) Therefore, apothem of hexagon = 8.46 cm then side of hexagon = apothem*2/sqrt(3) = 9.77 cm (approx) and so perimeter = 6*side = 58.63 cm
How do you find an apothem?
The formula for finding an apothem is s = 1/2 aP. S is the area, a is the apothem, and P is the perimeter.
The apothem of a regular pentagon is 10.8 centimeters what is the radius of the circumscribed circle?
The line joining the centre of the pentagon to any vertex is a radius of the circumscribed circle. The angle between such a line and the adjacent apothem is 360/10 = 36 degrees. If the radius is r, then we can now write: cos36 = 10.8/r So r = 10.8/cos36 = 13.350cm. to 3 decimal places.
What is the perimeter of a hexagon with an apothem of 12?
The perimeter of a hexagon with an apothem of 12 is 83.14
How do you find the apothem of an octagon with the diameter?
You can only do this for a regular octagon. It is much easier to understand the method if you do a rough sketch and follow the explanation using that. Unfortunately, this browser does not support any kind of drawing! Suppose the diameter of the octagon is D. Therefore the diameter of the circumscribing circle is also D. Form the centre of this circle, draw lines to two adjacent vertices of the octagon. The lengths of these lines is D/2 because these are radii of the circle. These lines and the side of the octagon form an isosceles triangle, and the apothem is the height of this triangle. Now consider half this triangle: the right angled triangle formed by the apothem, half the side of the octagon and the radius. The angles at the apex of the octagon is 360/8 = 45 degrees. So the angle at the apex of the right angled triangle is half that = 22.5 degrees. Then cos(22.5 deg) = Apothem/Radius So that Apothem = Radius*cos(22.5 deg) = D/2*0.9239 (approx).
How do you find the perimeter of a regular polygon with the apothem and area?
Perimeter = 2*Area/Apothem.
What does an apathum look like?
The apothem is the perpendicular from the cent of a regular polygon to one of it's sides. When drawn it looks like the line drawn for the radius or circumference of a circle.
What is an apothem of a regular polygon?
An apothem is a line segment from the center of a regular polygon to the midpoint of a side.
What is the apothem of a regular hexagon?
If the hexagon has side length s, then the apothem is sqrt(3) * s / 2.
