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it is also important to know the apothem This works for any regular polygon.Ĭhoose a side and form a triangle with the two radii that are at either corner of said side. Radius is the distance from the center to a corner. Each triangle has a side length s and height (also the apothem of the regular hexagon) of. Derivation of the area formulaĭivide the regular hexagon into six equilateral triangles by drawing line segments to opposite vertices. Using a grid made up of 1 mm squares is 10 times more accurate than using a grid made up of 1 cm squares. The smaller the unit square used, the higher the accuracy of the approximation. However, it is only an approximate value of the area. This method can be used to find the area of any shape it is not limited to regular hexagons. The regular hexagon to the right contains 17 full squares and 10 partial squares, so it has an area of approximately: The regular hexagon on the left contains 6 full squares and 10 partial squares, so it has an area of approximately:

The grid above contains unit squares that have an area of 1 cm 2 each. Below is a unit square with side lengths of 1 cm.Ī grid of unit squares can be used when determining the area of a hexagon. The area formula using the apothem is:Īnother way to find the area of a hexagon is to determine how many unit squares it takes to cover its surface. The apothem, a, of a regular hexagon is half of the distance between opposite sides of the hexagon. In such a case, the area of the hexagon is: Sometimes, in real life, it is easier to measure the distance between opposite sides of a regular hexagon. Plugging the side length into the area formula: Given that the perimeter is 72, the length of each side of the regular hexagon can be found by dividing the perimeter by 6, making each side length 12. Find the area of a regular hexagon that has a perimeter of 72.