Area And Perimeter Of Hexagon

Area of a hexagon

The expanse of a hexagon is the space contained within its perimeter. The grayness infinite is the expanse of the hexagon in the figure below.

Surface area formula of a regular hexagon

There are many unlike types of hexagons. The most common type is a regular hexagon, which is a hexagon that has sides of equal length and angles of equal measure.

The area, A, of a regular hexagon tin can be found given only its side length, s, with the formula:

Example:

Find the area of a regular hexagon that has a perimeter of 72.

Given that the perimeter is 72, the length of each side of the regular hexagon tin can be constitute by dividing the perimeter by vi, making each side length 12.

Plugging the side length into the area formula:

Sometimes, in real life, it is easier to measure the altitude betwixt reverse sides of a regular hexagon. In such a example, the area of the hexagon is:

The apothem, a, of a regular hexagon is half of the altitude betwixt contrary sides of the hexagon. The surface area formula using the apothem is:

Finding expanse using a grid

Some other way to detect the expanse of a hexagon is to determine how many unit squares it takes to comprehend its surface. Below is a unit of measurement square with side lengths of 1 cm.

A grid of unit squares can be used when determining the area of a hexagon.

The grid higher up contains unit squares that have an expanse of 1 cmⁱⁱ each. The regular hexagon on the left contains 6 full squares and ten partial squares, so information technology has an surface area of approximately:

The regular hexagon to the right contains 17 full squares and 10 partial squares, so information technology has an area of approximately:

This method can be used to find the surface area of whatever shape; information technology is not express to regular hexagons. Notwithstanding, it is only an approximate value of the area. The smaller the unit foursquare used, the college the accurateness of the approximation. Using a grid fabricated up of 1 mm squares is x times more accurate than using a grid made up of 1 cm squares.

Derivation of the expanse formula

Split up the regular hexagon into half-dozen equilateral triangles by drawing line segments to opposite vertices. Each triangle has a side length due south and tiptop (too the apothem of the regular hexagon) of . The area, A, of one of the equilateral triangles, drawn in blue, tin can be constitute using: