What is the area of a regular hexagon with a side length of 12 cm and an apothem length of 10.4 cm

Let's split the hexagon into 6 congruent isosceles triangles, with the lines joining the vertices to the centre. We know the vertical height of each triangle, which is going to be 10.4 cm (the apothem). To work out the area of a triangle, we just use (base x height)/2 

Using this formula, we get the area of 1 triangle to be:

1/2 x 12 x 10.4 = 62.4 cm^2 

Since we have 6 congruent triangles, all we have to do now is multiply this area by 6

So, we get 62.4 x 6 = 374.4 cm^2

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