copy-and-complete-the-tables-for-the-regular-polygons-shown-in-these-tables-p-represents-the-peri-17

Question

Copy and complete the tables for the regular polygons shown. In these tables,
$p$ represents the perimeter and $A$ represents the area.
$\begin{array}{|c|c|c|c|}\hline r & {a} & {p} & {A} \ \hline 6 & {?} & {?} & {?} \ \hline\end{array}$

Adam Cornes · Accepted Answer

gives us a regular polygon of three sides. In this case, it&#x27;s the triangle. So all sides are gonna be equal cause it&#x27;s regular. And I&#x27;ve just added a couple more notations are labeled all three cornice. I&#x27;ve also labeled the Points X is the center of the circle. In our was the midpoint for May to bay so little X is gonna be the land of 80 R. And little lazy apathy. Um, to the apathy, um is the perpendicular distance from the origin of the circle to the midpoint of the one side of the public gun. So we&#x27;re given that the radius of the Circle R is equal to six and we want to find the athm, the perimeter of the polygon on the area of the polygon. So first things first will find the athm. So what we can do is use trigonometry with news that the sign rule Stein Oh, oh, uh, we&#x27;ll find Well, that&#x27;s right. It was sign very every so we can rearrange Ferree. So a really cool It&#x27;s all right. Okay. Hey, this ah times are so we&#x27;ll need to find the angle. A. So what we can do is we know that the angle a next be it&#x27;s guns equal 360 divided by three, an ankle under the 20 degrees. We know that because we scroll up and imagine So that&#x27;s that&#x27;s the angle XB. So if you want to draw and three sides triangles, you get three triangles in the center and you know the degrees in the circle of 3 60 So you divide it by how on the sides or if you will triangles, and that will give you the angle of each 120. So we know that the angle X or we can do no it as a, uh, an equal half of that. Is it the straight line down there to the right angle So unequal don&#x27;t ever to ankles 60 degrees. Careful, we know that a so all angles in a triangle is gonna tow 1 80 degrees. So that means a is gonna equal 30 degrees, as we have 90 plus 60 could be 1 57 degrees remaining. So you pluck that into this equation, you should get a equals three. So that&#x27;s that. And then now we need to find the perimeter. So perimeter is going to be the number of sides. So in this case is three sides come up for the triangle times the length of one side. That&#x27;s going to be a big and we know a B is improvements to our So is the equivalent of eight R. Sorry, there&#x27;s three phones to they are not to show you why that is the ghosts of the midpoint. Just the midpoint. It&#x27;s going to be two of those to make hate today. That means is 68 NATO. We know it is little axe. And again you sign rule. So we rearrange the thanks in this little of equation here, so use this side of the equation and that sign. Thanks. Uh huh. That&#x27;s gonna equal three or a three. When you put these numbers in, man for a he&#x27;s gonna evil. 18 33 When you plug the numbers into this equation here for big and how old is left. As I said, the Arab other gun which will call it Hey, that&#x27;s all the apathy sounds a perimeter we pluck in Lawrence&#x27;s Hmm P uh, and a. So that&#x27;s gonna be, uh, times three. I&#x27;m 18 3 27 through three

Adam Cornes · Answer

given the regular polygon of six sides so hex again that&#x27;s inscribed inside a circle which is gonna have radio soft, which I&#x27;ll show here. I&#x27;ve just added some other notations in the diagram. So given point C and A for two points where beside me the circle be is the origin X is the angle are is the mid point A is the apathy, um, little ours radius would give in that a equal six. And the question and we need to find the radius that perimeter in the area of the pull A gun. So another thing we should do is find the angle. So we know that see, b A is going to equal 360 degrees degrees in the in the circle, divided by the number of triangles that will form in the circle from during these radius lines. Food lines like if you could form six and tables you divide by six vehicle 60 degrees and then we know that the angle that&#x27;s gonna be exactly half this because of you see the way it splits to me, that right angle so 62 unequal says he degrees. Therefore we can find a the angle as well. So that&#x27;s gonna be 1 80 Because we know that there&#x27;s 100 and 82 degrees in the triangle minus 1960 cools 30 degrees like that. So next thing we need to do is find the length of our so we can use sign roles that sign of Ah, okay. Handfuls. Fine. Thanks. And rank ankles sign. Well, hey, Avery. So we can rearrange this to find Are so our peoples sign of our which we know is 90 degrees under the signed of A, which we now know to be 30 degrees turns by a which were given in the question that you put those numbers in. You should get full room three now, what we need to do, we confined the perimeter. It&#x27;s a book. Before we need to do that, we need to find the length of sorry. This is going to be left. Lex here, That&#x27;s what. That lip. That&#x27;s what this little X was from that. So can you sign weekend, find a little less that&#x27;s gonna be signed. I have a sign. Thank hands by a basing to three. So then the perimeter is going to be the number of sites about six times by the length. Oh a to C See that Let the Red Sea, which is going to be the same as two X Could you see? That&#x27;s the midpoint There you can rewrite our six times Teoh plank act includes 12 ex army, no excess to re three set us equals 20 full room three. That&#x27;s a permit. Now we confined theories pull a gun was wholly t cheers using the former half a times, the perimeter, my complete values in, say, 24 e three in the value I&#x27;m very which, given its style six. So you put those in, you should get 72 3

Amrita Bhasin · Answer

given this information that we have, we we can tell from looking at the problem that A is gonna be 1/2 a p, which is gonna be 1/2 times three over two times p, which I&#x27;ve written up here is mine sward of three, which gives us 27 squirt of three over four. So a is 27 scored a few over four and are is three a, which is three over two.

Amrita Bhasin · Answer

Okay. We know that A is five squirt of three different of the R is too over squared of three A. And given this, we know that we are playing in five scored a free for a so it&#x27;s too over squared of three times five Spurt of three, which is equivalent to tough. Okay, we know that P is six are so six times 10 is sexy. Capital A is 1/2 a P shows 1/2 times five squirt of three from 60 which is 150 cc&#x27;s. It&#x27;s standard divide by two square root of three.

Problem

Copy and complete the tables for the regular poly…

Problem 5 Medium Difficulty

Copy and complete the tables for the regular polygons shown. In these tables,
$p$ represents the perimeter and $A$ represents the area.
$\begin{array}{|c|c|c|c|}\hline r & {a} & {p} & {A} \\ \hline 6 & {?} & {?} & {?} \\ \hline\end{array}$

Answer

the required value of $a$ is ${3}$ $p$ is ${18 \sqrt{3}}$ and $A$ is $27 \sqrt{3}$

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

Geometry

Megan C.

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the required value of $a$ is ${3}$ $p$ is ${18 \sqrt{3}}$ and $A$ is $27 \sqrt{3}$

Geometry

Megan C.

Christine G.

Kristen K.

Michael D.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

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

Megan C.

Christine G.

Kristen K.

Michael D.

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

Geometry