It is always a good idea to divide the geometric shapes that have many sides into more manageable shapes such as triangles since there are many ways of calculating their area. Splitting a regular hexagon into triangles simplifies everything since the triangle formed this way are all equilateral.
The 6 triangles formed are equilateral which means that all their sides are equal in length. All of the 6 triangles are also identical. To calculate area of the regular hexagon we have to find area of one of the equilateral triangles and multiply it by 6.
For this example let’s consider that the length of hexagon’s side is 6 units
The equilateral triangle AGF is divided by its height into 2 identical right angled triangles. Using Pythagorean theorem we can find the length of AH which we will use in next step to calculate the area of the equilateral triangle AGF.
AG2 = AH2 + GH2
AH2 = AG2 - GH2
AH2 = 62 - 32
AH2 = 36 - 9 = 27
AH = 5,2
Area of the triangle AGF is calculated by multiplying the base AF by the height GH then divide the result by 2.
Area (AGF) = (AF × GH) ÷ 2 = (6 × 5) ÷ 2 = 30 ÷ 2 = 15 square units
All we have to do is to multiply the area of the triangle AGF by 6 (since the hexagon is made of 6 identical triangles).
That means the area of the hexagon is 90 square units.