Other Polygons - Math

To find the side length from the area of an octagon and the apothem we must use the area of a polygon which is

First plug in our numbers for area and the apothem to get

Then multiply to get

Then divide both sides by 4 to get the perimeter of the figure.

When we have the perimeter of a regular polygon, to find the side length we must divide by the number of sides of the polygon, in this case 8.

After dividing we find the side length is

The equation to calculate the magnitude of an interior angle is , where is equal to the number of sides.

For our question, .

To find the angle of any regular polygon you find the number of sides, . In this example, .

You then subtract 2 from the number of sides yielding 5.

Take 5 and multiply it by 180 degrees to yield the total number of degrees in the regular heptagon.

Then to find one individual angle we divide 900 by the total number of angles, 7.

The answer is .

The sum of the exterior angles of any polygon, one per vertex, is . As each angle measures , just divide 360 by 1.5 to get the number of angles.

To find the angle of any regular polygon you find the number of sides , which in this example is .

You then subtract from the number of sides yielding .

Take and multiply it by degrees to yield a total number of degrees in the regular nonagon.

Then to find one individual angle we divide by the total number of angles .

The answer is .

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 17 to get the measure of one exterior angle:

The sum of the measures of the exterior angles of any polygon, one per vertex, is . In a regular polygon, all of these angles are congruent, so divide 360 by 23 to get the measure of one exterior angle:

The measure of each interior angle of a regular polygon with sides is . We can substitute to obtain the angle measure:

The easiest way to answer this is to note that, since an interior angle and an exterior angle form a linear pair - and thus, a supplementary pair - each exterior angle would have measure . Since 360 divided by the number of sides of a regular polygon is equal to the measure of one of its exterior angles, we are seeking such that

Solve for :

The polygon has 20 sides.

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long . The left and right sides would be 11 units long . Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

To find the perimeter of a regular polygon, we take the length of each side, , and multiply it by the number of sides, .

In a nonagon the number of sides is , and in this example the side length is .

The perimeter is .

To find the perimeter of a regular hendecagon you must first know the number of sides in a hendecagon is 11.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is .

The answer for the perimeter is .

The formula for the perimeter of an octagon is .

Plugging in our values, we get:

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long . The left and right sides would be 11 units long . Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

To find the perimeter of a regular polygon, we take the length of each side, , and multiply it by the number of sides, .

In a nonagon the number of sides is , and in this example the side length is .

The perimeter is .

To find the perimeter of a regular hendecagon you must first know the number of sides in a hendecagon is 11.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is .

The answer for the perimeter is .

The formula for the perimeter of an octagon is .

Plugging in our values, we get:

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long . The left and right sides would be 11 units long . Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

To find the perimeter of a regular polygon, we take the length of each side, , and multiply it by the number of sides, .

In a nonagon the number of sides is , and in this example the side length is .

The perimeter is .

To find the perimeter of a regular hendecagon you must first know the number of sides in a hendecagon is 11.

When you know the number of sides of a regular polygon to find the perimeter you must multiply the side length by the number of sides.

In this case it is .

The answer for the perimeter is .