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amyseal
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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rohiraakshay4

The area of a regular hexagon with a side length of 12 cm and apothem length of 10.4 cm is 374.4 cm^2.

Regular Hexagon:

Regular hexagon is a polygon with 6 sides.

All the sides and measurements of all the angles are equal.

An apothem is line segment from the center of a polygon to the middle point of any one side.

Here we have given

Apothem = 10.4 cm

length of side = 12 cm

How to find area of regular hexagon?

Divide the hexagon into 6 congruent isosceles triangles, with lines connecting the vertices to the center. Each triangle's vertical height will be 10.4 cm, as we know (the apothem). We just divide (base x height) by 2 to find the area of a triangle.

The area of a triangle is calculated using this formula:

1/2 x 12 x 10.4 = 62.4 cm^2

All we need to do now is multiply this area by 6 because we have 6 congruent triangles.

62.4 x 6 = 374.4 cm^2

Hence the final answer is 374.4 cm^2

Learn more about regular hexagon here-

https://brainly.com/question/1969956

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