How to Find Apothem of a Regular Polygon

Enter the given values and click calculate button to find the answer. This is a little trickier to calculate than the perimeter.

Apothem Of A Regular Polygon Calculator Math Calculator Regular Polygon Online Math

R r radius.

. An apothem of a regular polygon will always be a radius of the inscribed circle. First start with the formula for the area of a regular polygon. We can use the apothem area formula of a polygon to calculate the length of the apothem.

The apothem a can be used to find the area of any regular n-sided polygon of side length s according to the following formula which also states that the area is equal to the apothem multiplied by half the perimeter since ns p. Below is the process of how to find the apothem of a polygon. The apothem formula when the radius is given is.

A is the apothem which is a line from the center of the polygon to the middle of any of its sides. Substituting 20 for N gives us 202 180 3240 degrees as the SUM of all the angles. N is the number of sides of the regular polygon.

In the figure we see the polygon can be divided into n equal triangles. Area ap² n tanπn Where. The apothem formula when the radius is given is.

Use the formula that uses the facts you are given to start. A Side length. So angle t 180n.

You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem. Divide the number of sides into 360 to get the interior angle related to each side. So h a 2tan t here h is the apothem so apothem.

If you know the length of one of the sides the apothem length is given by the formula. Apothem given the length of a side. EqA frac12cdot acdot P eq where.

P is the perimeter. N Number of side. The word apothem can refer to the line.

Ap is the apothem the segment connecting the side midpoint to the center. A 12 a p. The area of an n-sided regular polygon with its side length s and apothem a is given by.

Area n a ri 2 having ri - incircle radius its also an apothem - a line segment from the center to the. Here we divide the pentagon into five congruent triangles and use one of the triangles to find the apothem. A n s a 2 A n s a 2 where n n is the number of sides s s is the length of one side and a a is the apothem.

Area perimeter ri 2 given ri and polygon perimeter. We can see that the apothem is the height of one of the triangles. The formula is apothem s 2 tan 180 n displaystyle textapothemfrac s2tanfrac 180n where s displaystyle s equals the side length of the polygon and n displaystyle n equals the number of sides the polygon has.

We go through an example in this video involving an octagon with an apothem of 6 uni. The length of the side s divided by 2 times the tangent tan of 180 degrees divided by the number of sides n. Where r Radius of Polygon n Number of Sides of a Polygon cos Cos function calculated in degrees Use our below online apothem calculator to find the apothem of the given polygon.

R Apothem of regular polygon. So we just need to divide 360 by 18 and find there are 20 sides to the polygon. The length a of the apothem of a regular polygon with n sides can also be expressed using the measure of the radius of the circle circumscribed around the polygon.

To find the formula for the apothem we can use the diagram of a pentagon. Area n ri² tan πn given ri. C o s 180 n.

N n number of sides. Looking into one of the triangles we see the whole angle at the centre can be divided into 360n. How do you find the area of a regular polygon with only the apothem and number of sides.

The formula for calculating the length of the apothem is this. How to Calculate Apothem of Regular Polygon. Each formula below shows how to find the length of the apothem of a regular polygon.

A a rcos180 n r. Set up the formula for finding the apothem of a regular polygon. Alternatively if we know the circumradius radius of the polygon we can use this below formula to find the apothem.

In the case of a parallelogram each pair of opposite sides is the same length so the perimeter is twice the base plus twice the side length. How do you find the area of regular polygons. Learn how to find the area of a regular polygon given only the apothem.

N n number of sides of a polygon. The apothem of a regular polygon is the shortest distance from the center point to one of the sides creating a right angle. By definition all sides of a regular polygon are equal in length.

If you know the apothem of a regular polygon you can compute the area with the formula. Apothem of Regular Polygon calculator uses Apothem Side 2 tan 180 pi 180 Number of Side s to calculate the Apothem Apothem of Regular Polygon is defined as the distance between the center of the regular polygon and the midpoint of a side provided the value of side length for calculation. Each formula below shows how to find.

Cos C o s cosine function which is calculated in degrees. If you want to check this use the formula for the sum of all interior angles of a regular polygon which is N-2 180 where N is the number of sides. Now tan t a2h.

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