find-the-area-of-each-polygon-a-regular-hexagon-with-perimeter-72-2

Question

Find the area of each polygon.
A regular hexagon with perimeter 72

Adam Cornes · Accepted Answer

right hex again. This inscribed inside of circle with radius are just on the diagram of what I would look like. There&#x27;s a brooks kept, so the APA theme will be here. So that&#x27;s gonna be the perpendicular distance from the origin to the center of the side. The polygon, they&#x27;re X is the distance from P to the midpoint and little eyes, the radius paying here where they took society, the circle. And we need to find the perimeter. So given the perimeter was seventy two and we can immediately equate that because we knew the former That is gonna be the number of sites which is six times by the length of one sciences he keep. You can see that peak who is just two times that schools are is the midpoint that&#x27;s gonna be sick. I was too an ankle twelve. Thanks That we can then work our angles to figure out the size of X. So the angle of okay, x Q Simply going to be the degrees in a circle three, then sixty divided by six Munchen with the drop A with these radius lines, I mean, a round circle will have six triangles like that Sure that So it&#x27;s simply three and sixty. Divided by six is gonna get sixty degrees to the angle X, which is gonna be this angle here. That&#x27;s gonna be exactly half of that. As you can see, it&#x27;s split by the apathy. So in the people sixty degrees, three side, what about two? That&#x27;s C degrees. So we can then use sign role to quit that. But before we do it, we can figure out the angle of peace. So that&#x27;s not P for the perimeter. That&#x27;s little pee there. So that&#x27;s gonna we know that there&#x27;s one hundred and eighty degrees in a triangle. So with one eighty minus the Angola, which is ninety minus the angle at X, which were just noticed thirty degrees, which will equal sixty degrees. And now it can you sign role so side of hey again, That&#x27;s not the perimeter and equal sign o X X equals sign. Well, uh, we can rearrange these to find a and so it&#x27;s gonna be a sign of hay plans by X. So sorry, that&#x27;s gonna be big accent. Yeah, a little X, which we know those angles now that we&#x27;ve just figured out above here. That&#x27;s gonna hungry. Found out. Um, what X is gonna equal? So that&#x27;s going to be six three. Just her line. Do you that we know that axes six. Because if we rearrange this top equation head, we know that twelve x four seventy two so x sex. So we conclude this into our area, but the public grants That&#x27;s really call that a b so off of the APP thing. So this is P for the permits and little pay. So what? There&#x27;s in? Oh, I&#x27;m saying it&#x27;s great. Already finds by anti to print and people two hundred sixteen breakthrough That&#x27;s final inside.

Amrita Bhasin · Answer

Okay. We know that a is for you know, the US is to over square root of three. Hey, which is to over swear to three terms for which is a over spurt of three. You know that he is six ass, which is we just figure out what s is six times eight divided by square root of three is 48 cause it&#x27;s something is 48 divide best part of three. You know that capital is 1/2 a p, which is 1/2 comes eight over. Spurt of three comes 48 over square root of three, which is gonna be for term 16 over three. Because we had 48 over here. What? We crossed it off. Consistent temperature is 48. This is simply 64.

Michelle Nguyen · Answer

here. We haven&#x27;t gone with the perimeter of 72 so each side of the octagon is going to be fine. So our triangle is 30 16 90 and we need to find out how much is each angle. So 3 60 divided by age, and that&#x27;s gonna give us 45. And then we need to divide that by two, and we get 22.5. Wanted take tangent of 22.5 is equal to 4.5, which is half of the side over X. Defying the A possum before five, divided by tangent of a 22.5 and are a possum is 10.86 when a plug into our Formula 1/2 times perimeter, which is 72 times a papa is 10.86 and that is going to give us our area of 3 91 point

Ethan Somes · Answer

So here we have a hexagon. This is a regular X. Come. So the sides are all the same length, even if they don&#x27;t look like it. Um and we know the side length is 12. And now I can break a hexagon nicely up into I am Sam. Equal lateral triangles. Now, how do I know that you collateral? Well, the central angle here is 366 and go all the around 36 degrees. And if I divide 3 60 divided by six, I got each of these is 60 degrees. And now I know that all of these, um radi I of this are going to convince from the center. And so these two angles must be computed. Well, so, um, we have 60 plus two times. Some angle will be equal to 100 82 angles. Add up to 180 in a triangle, so we end up with two X equals 1 20 So x will also be sixties. We have 60 60 60 and that is the collateral triangle. So now, um, we have an equal lateral triangle with a base length of 12 a side length of 12 and we need to find the height. So to do that well, Hind, that will have the base like this six. And now we have this right triangle with two sides, two legs of six and each and a hypotheses of 12. I can use the cutback mean belong to, say, six squared. Plus each squared equals 12 square. So 36 plus speech squared will be ableto 1 44 Subtracting 36 from both sides gives me that beach squared is equal to, um wanna wait. And that means each is the square root. One night I&#x27;ll leave that for now. Okay, now we know that. So we confined the area of this triangle. And there&#x27;s six of those triangles in our hex a gram. So area will be six times the area of that triangle, which is 1/2 the base, which is 12 times the height, which is the square root of one of eight. So doing this have been do six times 12 times half I get 36 Route 108 And when we multiply that out, we get 3 74.12 What was our unit? Centimeters squared

Problem

Find the area of each polygon. A regular hexagon…

Problem 15 Hard Difficulty

Find the area of each polygon.
A regular hexagon with perimeter 72

Answer

the required area $A$ of the regular hexagon with perimeter 72 is 216$\sqrt{3}$

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Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Geometry

Lily A.

Catherine R.

Samuel H.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

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the required area $A$ of the regular hexagon with perimeter 72 is 216$\sqrt{3}$

Geometry

Lily A.

Catherine R.

Samuel H.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

Ray C. Jurgensen,Richard G. Brown,John W. JurgensenGeometry

Lily A.

Catherine R.

Samuel H.

Michael D.

Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Geometry