Question

Use the diagram of the regular hexagon to support an explanation showing why the formula accurately yields the area of the hexagon. (Recall that a is the apothem and P is the perimeter of the hexagon.)

Answer 1

which formula
I can tell you then

Answer 2

It doesn't tell me a formula. Just the picture.

Answer 3

Well I assume the formula is \[\frac{ 1 }{ 2 }ap\]

Answer 4

why do you need a formula?

Answer 5

The formula is needed so because it is what you are proving to why it yields the exact area

Answer 6

So a regular hexagon contains 6 congruent triangles

Answer 7

To the area of a triangle is \[\frac{ 1 }{ 2 }bh\] but in this case there are 6 of them

Answer 8

By them I mean triangles

Answer 9

So how would you do this, find the area of one of the triangles and multiply it by 6 right, because that is the number of triangles in a hexagon

Answer 10

So you would get\[6\frac{ 1 }{ 2 } bh\] but remember that the base is one side of a hexagon so therefore if you multiply that side by 6 you would get the perimeter.

Answer 11

So this would simplify to \[\frac{ 1 }{ 2 }ap\]

Answer 12

okay but its asking me to explain.

Answer 13

Yeah use the explanation I gave that would work

Answer 14

to support an explanation so i would write that?

Answer 15

Yes basically

Answer 16

Do you think it will be the correct answeR?

Answer 17

Yes it would because to prove the area using apothem's and perimeter's this would be the only formula

Answer 18

okay thanks!

Answer 19

You're welcome.

Answer 20

I am having a little bit of a hard time of how i should put that into words.

Answer 21

@Brill