1. Sandra and Jerry Hampton built a deck in the shape of a regular hexagon off the back of their new home. The sides of the hexagon are 14 feet long. The couple has decided to apply water sealant to the surface of the deck to protect it from the elements. The Hamptons have already spent more than they had planned on for their new deck and they have only $30 left of their budget. The couple needs to determine the total area of the deck in order to know how much sealant to buy. What is the area of the Hampton's deck?

Question

hero · Answer

Hints:

1. Divide the hexagon to six triangles
2. Use the formula for area of an equilateral triangle:
$A = \large\frac{\sqrt{3}}{4}a^2$, a = length of one side

anonymous · Answer

So if I divide the triangle into 6 pieces ... I only know the base which is 14. I don't know the height :(

hero · Answer

Using the formula I provided you with is an alternate way to find the area of an equilateral triangle without needing to know the height.

anonymous · Answer

I got area= 36.75 ? Is that correct? @Hero

hero · Answer

I'm not sure how you got that

hero · Answer

That is not what I got

hero · Answer

Remember, the formula that I gave you is the formula for only one of the triangles within the Hexagon. There are six regular triangles in the hexagon.

anonymous · Answer

Okay, so I did the square root of 3 / 4 =.866025
I then multiplied that by 196 and now got 170 ft?

hero · Answer

Thats not what I got

anonymous · Answer

What are you getting? hmmm~

anonymous · Answer

Am I forgetting to multiply the answer by 6?

hero · Answer

I got something else for the area of the triangle even before multiplying by six.

hero · Answer

$\frac{\sqrt{3}}{4} \times 14^2$

anonymous · Answer

What are you getting? Did you get something close to: 3055 ?

hero · Answer

What kind of calculator are you using?