See all Speciality Lodging in Punakaiki. The Hexagon.
Lowest prices for your stay. Guests 1 room , 2 adults , 0 children Guests 1 2. Show Prices. Like saving money? We search up to sites for the lowest prices. Full view. View all photos 10 It's set right on the coast, at the mouth of the Fox River and just 10 minutes from Punakaiki the site of the famous 'Pancake Rocks'. It's the perfect place to take time out, rest and soak up the breathtaking coastal scenery of the wild West Coast. Read more. Property amenities. Free parking. Room features. Good to know. Getting there. Westport Airport 35 km. Nearby restaurants. Rusty Cup Cafe.
Nearby attractions. Truman Track. Fox River Cave Walk. Traveller rating. Time of year. Traveller type. Selected filters. Fiona J wrote a review Oct Wonderful break from the city. We had a fantastic stay at the Hexagon. See what's up for this year! Check out the Hexagon archives in our Photo and Video Galleries, featuring our About Hexagon Hexagon is a nonprofit organization composed of people whose purpose is to create and stage an original, political, satirical, musical comedy revue each year, both to have fun entertaining and to raise money for local charities.
Get Hexagon Stuff and Help! So we can use that information to figure out what the other angles are. Because these two base angles-- it's an isosceles triangle. The two legs are the same. So our two base angles, this angle is going to be congruent to that angle.
If we could call that y right over there. So you have y plus y, which is 2y, plus 60 degrees is going to be equal to Because the interior angles of any triangle-- they add up to And so subtract 60 from both sides. You get 2y is equal to Divide both sides by 2. You get y is equal to 60 degrees. Now, this is interesting. I could have done this with any of these triangles. All of these triangles are triangles, which tells us-- and we've proven this earlier on when we first started studying equilateral triangles-- we know that all of the angles of a triangle are 60 degrees, then we're dealing with an equilateral triangle, which means that all the sides have the same length.
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So if this is 2 square roots of 3, then so is this. This is also 2 square roots of 3.
And this is also 2 square roots of 3. So pretty much all of these green lines are 2 square roots of 3. And we already knew, because it's a regular hexagon, that each side of the hexagon itself is also 2 square roots of 3. So now we can essentially use that information to figure out-- actually, we don't even have to figure this part out.
I'll show you in a second-- to figure out the area of any one of these triangles. And then we can just multiply by 6. So let's focus on this triangle right over here and think about how we can find its area. We know that length of DC is 2 square roots of 3.
We can drop an altitude over here. We can drop an altitude just like that.
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And then if we drop an altitude, we know that this is an equilateral triangle. And we can show very easily that these two triangles are symmetric. These are both degree angles. We know that these two are degree angles already. And then if you look at each of these two independent triangles, you'd have to just say, well, they have to add up to So this has to be 30 degrees.
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This has to be 30 degrees. All the angles are the same. They also share a side in common. So these two are congruent triangles. So if we want to find the area of this little slice of the pie right over here, we can just find the area of this slice, or this sub-slice, and then multiply by 2. Or we could just find this area and multiply by 12 for the entire hexagon. So how do we figure out the area of this thing? Well, this is going to be half of this base length, so this length right over here. Let me call this point H. DH is going to be the square root of 3. And hopefully we've already recognized that this is a triangle.
Let me draw it over here. So this is a triangle.