Question

How would I do this? You are planing to use a ceramic tile design in your new bathroom. The tiles are blue and white with equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measure 7 centimeters, what will be the exact area of each hexagonal shape?

Answer 1

Equilateral Triangle.
Each side is length 7.
Equiangular Triangle.
Each Angle is 60º.
Median = Angle Bisector = Perpendicular Bisector = Altitude
Draw just one Altitude in one triangle and you should see a 30-60-90 Right Triangle.
You should see that you have 11 others just like it.

Answer 2

I got 21.

Answer 3

I didn't get anything. I'm waiting to see your work.

Answer 4

Nvm, i see what i did. One sec

Answer 5

21 is in the neighborhood of the area of ONE of the equilateral triangles. It is not good enough for ANYTHING about this problem except maybe spray-painting the design when it is done.

Answer 6

I got 254.61.

Answer 7

Really, if you showed your work, I could tell you where you wandered off.

Answer 8

Well i got the height of the equilateral triangle by doing 7 times sin60 and got 6.06.

Answer 9

You need to give up your calculator. Go hit it with a hammer, or something.

The height is \(\dfrac{7}{2}\sqrt{3}\).

Go on. What was next?

Answer 10

Haha ok, I do that times 7. and then by 6?

Answer 11

Please provide the formula for the area of a triangle.

Answer 12

1/2 times base times height

Answer 13

You don't seem to have used the "1/2" in your problem solving.

Answer 14

I accidentally forgot to write it down but I know it

Answer 15

Okay, use that and revise your answer.

Answer 16

73.5sqrt3

Answer 17

There we have it. I get \(\dfrac{147}{2}\sqrt{3}\) (If you like = 127.3057343563)