 A heptagon is a type of polygon with 7 sides. There can be regular and irregular heptagons. With a regular heptagon, all of the sides are an equal length and the angles are going to be the same. When the length of the sides for a regular heptagon are given, it is possible to determine the perimeter, apothem, and the area of the heptagon.

Angles for a Heptagon

In a regular heptagon, all of the sides are the same length so all of the angles are going to be the same as well. The interior angles add up to 900 degrees and each one is 128.57 degrees. The central angles (those on the center point of the heptagon) are all 51.43 degrees. These are both true for any size heptagon, so long as it is a regular heptagon. Irregular heptagons can have various side lengths and angles.

Determining the Perimeter of the Heptagon

When the length of the sides is given, determining the perimeter is done by multiplying 7 (the number of sides) by the length of the side. If the side is 11, the perimeter is 77.

Determine the Apothem of the Heptagon

When viewing a regular heptagon, the line going from the center point to the middle of one of the sides is the apothem. This is needed to determine the area of the heptagon. As long as the length of the sides is known, the apothem can be determined by using the formula: apothem= s/2 tan (180/n). In this formula, “s” is the length of the sides and “n” is the number of sides. If the sides of the heptagon are 7, for example, the formula would be filled out as apothem=7/2 tan(180/7). This would end up with the apothem being 7.268.

Determining the Area of the Heptagon

Learning how to find the area of a heptagon includes learning the previous formula as well as the one for finding the area. The apothem of the heptagon must be found before the area of the heptagon can be found. The formula for this is Area=(1/2)nsr. In this case, “n” is the number of sides, “s” is the length of the sides, and “r” is the apothem. Using the same example above, with the side as 7, the area formula would be worked as follows: Area=(1/2)(7)(7)(7.268). So, the area for this example would be 178.066.

When the Heptagon Isn’t Regular

Regular heptagons have angles and sides that are all the same. This means there is a center point that can be found. With irregular heptagons, since the angles and sides can all be different, there is not generally a center point.

Overall, learning how to find the area of a heptagon involves a few steps, but it is possible to do when the person knows the length of the sides. Provided the heptagon is a regular heptagon, the previous steps can allow a person to find the perimeter, apothem, and the area.