# How do you find the area of a regular hexagon with an Apothem?

## How do you find the area of a regular hexagon with an Apothem?

Apothem is the line segment that is drawn from the center of the hexagon and is perpendicular to the side of the hexagon. We can find the area of a regular hexagon with apothem using the formula, Area of hexagon = (1/2) × a × P; where ‘a’ is the apothem and ‘P’ is the perimeter of the hexagon.

How do you find the area of a polygon with only the Apothem?

You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.

### How do you find the area of a hexagon with an apothem of 6?

The area of a regular hexagon is 6 areas of equilateral triangles with a side equal to a side of a hexagon. Each such triangle has base a=4√3 and altitude (apothem of a hexagon) h=a⋅√32=6 .

Is the apothem equal to the side?

Is the Apothem Equal to the Side Length? No, an apothem’s length is not always equal to its side length. However, if we know the side length of a polygon, the apothem can be calculated.

## What is the formula for finding the area of a regular polygon with perimeter and apothem length?

The area of any regular polygon is given by the formula: Area = (a x p)/2, where a is the length of the apothem and p is the perimeter of the polygon.

How do you find the area of a regular pentagon with the apothem?

The formula that is used to find the area of a pentagon using the apothem and side length is, Area = 5/2 × s × a. Here, “s” is the side length and “a” is the apothem of the pentagon.

### What is the area of a regular hexagon with apothem 7.5 inches?

112.5√3
Since the area of a triangle is (12)⋅b⋅h , then the triangle’s area is (12)(15√33)⋅(7.5) , or 112.5√36 . There are 6 of these triangles that make up the hexagon, so the area of the hexagon is 112.5⋅√3 .

What is the formula for the area of a hexagon?

Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle. The formula for finding the area of a hexagon is Area = (3√3 s2)/ 2 where s is the length of a side of the regular hexagon.

## How do you calculate the dimensions of a hexagon?

Because a regular hexagon has six sides of the same length, finding the length of any one side is as simple as dividing the hexagon’s perimeter by 6. So if your hexagon has a perimeter of 48 inches, you have: 48 inches ÷ 6 = 8 inches. Each side of your hexagon measures 8 inches in length.

What are the dimensions of a regular hexagon?

A hexagon has exactly six vertices. A hexagon is a six-sided, two-dimensional shape. A regular hexagon consists of six equal sides with internal angles of 120 degrees, while an irregular hexagon can have sides and angles of any size.

### How do you find the radius of a hexagon?

The radius length allows the hexagon to be divided into six equal triangles that help in calculating the area of the hexagon. By using the area of the hexagon and the trigonometric properties of the inner triangles, you can find the radius of the hexagon.

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