find-the-area-of-each-polygon-an-equilateral-triangle-with-radius-4sqrt3-2

Question

Find the area of each polygon.
An equilateral triangle with radius 4$\sqrt{3}$

Adam Cornes · Accepted Answer

electoral triangle that&#x27;s inscribed in a circle. And I&#x27;ve just added some extra notation to the diagram. So the O it&#x27;s going to be the center of the circle The P asking here whether corners of the public on meet the circle Andi are is the midpoint is the apathy little Liza Radius, that you can see me in these points. So we&#x27;re given that the radius equals 43 have shown the formula for the area of the polygon which are Paul. Hey, pay. And so what we can do first to start off with is find the angles to help us work. How? The length of the sides. So the angle um be sorry. The urgent circle off dinner is access A P. Thanks s gonna ankle 360. The amount degrees in a circle provided by three, 120 degrees to the reason that&#x27;s three is If you imagine the line all the radius circled, it would make three triangles. So will be these angles here. That&#x27;s the PXs one that on there. So compared to that. So this is the pay accessible and that&#x27;s 120 degrees. So we know that the angle, it&#x27;s gonna be half of that. You can see where it split, where it goes to the app within their but that line, that&#x27;s kind of 100 20 over to. We&#x27;re just gonna ankle 68 degrees. So then we can use the angle. Oh, because we know that there&#x27;s 180 degrees in the triangle. So you want 80 minus that, right? And real 90 But 60 Grady&#x27;s. And I am thankful that he degrees and then we can use sign rolled to figure out thes length of sides now, so you know that signed. Oh, it&#x27;s every red. Well, some you, uh, so that&#x27;s big on that, uh, equals sign. Oh, I have a right. So we re arrange. We knew that. Any sign? Oh, I have a sign. And, uh, times. Ah, but those numbers in because we know what those are we know. Oh, you know, uh, we know little. Uh, that&#x27;s gonna come out 2 to 3. We do the same acts. Will be sign ex something. Ah. Oh, but there&#x27;s And at six, this isn&#x27;t a And then we know that the era of the probably gun is made of the perimeter. Say the perimeter is gonna eat with the number of size, which is three kinds of length of one side, which is going to be pizza ass. We know that piece ass is the same as two X three times. You know, it&#x27;s not just shape. Why, That is a diagram. This is excess. And we noticed that they are is the mid plane. So it&#x27;s gonna be to those that&#x27;s a full six acts We just worked on act, You know that last April 36. Now we can finally figure out there the color gun Times A and A include those numbers in 30 sets.

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.

Rishi Kavikondala · Answer

the area formula for a regular polygon is 1/2 times the apple thumb times the number of sites times decide life. And for the case of a triangle, you have a equals. The Appleton Times three times s drying out our regular triangle. Here we have a If this is our base and this is half the base right here with this being the whole base, the app with, um would simply be actually, let&#x27;s just call this s the app with, um would simply be s times the square of rs over too. Times the square root of three because of the special right triangle rule for 30 60 90 triangles, 1/2 times s over two squared of three times s and multiplying everything out. That gives you s squared times the square root of three over four and looking at the formula provided in the problem, you see that it is 1/4 times s squared times the square root of three. And as you can see, these two formulas are in fact equivalent. So the area of an equilateral triangle can be found using this formula or this one as they&#x27;re the same

Natalie Daly · Answer

Okay, So for this problem were given unequal lateral triangle on tool that it&#x27;s apathy. Is Tuffey. So here I drew diagram, um, showing it up with them two feet. We&#x27;re told to find the area of this triangle just given this information. So one helpful formula from the chapter that we can use is that the area of any polygon is people to 1/2 its apathy on times its perimeter. Um, this works because it&#x27;s triangle was an equal at area of a triangle and, uh, another formula that we can use Selves problems that the perimeter of equal lateral triangles equal to three times its site length, uh, one of the side. Thanks. So, um, our first step in solving this is to draw a line from the center point to a nearby for attacks in this line is going to buy set an angle that we have right here. Uh, and we know every angle in an equilateral triangle. 60 degrees. So when you bi sect that you create this single 30 degrees. Oh, and what we can do a spring this triangle down here, we&#x27;ll make it bigger. Use your seat. We now have this new mini triangle within it in which this angle is 30 degrees since 90 and pissing gore here is 60 degrees. Uh, this is still two feet. So sorry, we ve right that this is still two feet to two feet. Here we go. Um, and we know that this length right here is 1/2 truly of aside because the app thin will always, uh, intersect from will always be from the center point to midpoint of one of the sides of the triangle s. We know that this this would be when half the length of a side of the triangle, um and we can use the properties of our 60 30 90 triangles, which are remind you of if we have this and I&#x27;ll call this late backs, then we know that this right here his Route three x So if we&#x27;re given that X is two feet and we want to find one, have s we know that that&#x27;s equal to root. Three X, which is 1/2 mess, is equal to root three times two feet. Um, so we know that the sideline will be you will, too for route three and our units or feet. So each side of that triangle, not the smaller want. The bigger one is, uh, equal lettering. Triangle is fourth times route three feet. Mom, um, so we can play this information to find the perimeter coronaries equal to three s sequel to three for route three, um, which is equal to 12 route three feet. And I think we both know that, uh, what the feminists and the kroner. We can just plug this into original area equation. So the area this equal lateral triangle is 1/2 her up some of two feet time or Perathoner, the 12 route three feet, which is equal to 12 route three feet squared. And for running Teoh the 10th we just multiply using our calculators. Um, we will multiply 12 times rectory and get that. Our answer is 20 point eight. Once you ran to the temp, so feet squared, and that&#x27;s gonna be the area of our collateral

Ashley High · Answer

So this problem? I haven&#x27;t Nikoleta RL triangle inside a circle. So what we&#x27;re gonna do is find the area of the circle, subtract the area of the triangle, and that will give me all the areas of those, um, of those arcs of one of those segments. But I only need one of them. So after I do that, I&#x27;m gonna divide it by three just to find one of those areas. So let me draw my picture here. I have my circle, and then I have a triangle. No, no, this is the re. So each of my angles and my travel is 60 because they&#x27;re equal lateral. So this one&#x27;s being cut in half when I draw this line. So that means this angle is 30. And this angle is 60 up here. So now I know the side across from 30 is three. The side across from 90 is going to be six and side across from 60 is three scripts of three. So now I know the radius of my circle. It&#x27;s six. See that so defined the area of my circle. I&#x27;m gonna do pie. Our, which is six squared. So their, um of circle is 36 pie now the area of my triangle. So for my triangle, any of a base in my height. So what I have here is I know that my base this I would be through scripts of three as well. So if I was to extend this here, I know that this angle is 60. Now this Inglis 30. So the side across from 30 is three skirts of three. Now the side across from 60 is going to be three skirts of three times screwed of three. Which leaves me with three times three, which equals nine. So my height is nine. So the base of my triangle is six words of three. My height is nine and I divide by two. So that leaves you with 27 skirts of three for my triangle. So I have 36 pi minus 27 skirts of three. And then I&#x27;m dividing everything by three. So 36 pie, divided by three is 12 pie and 27 divided by three is nine. So the area of that one shaded region is 12 pi minus nine skirts of three

Problem

Find the area of each polygon. A square with rad…

Problem 13 Easy Difficulty

Find the area of each polygon.
An equilateral triangle with radius 4$\sqrt{3}$

Answer

the required area $A$ of the equilateral triangle is 36$\sqrt{3}$

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the required area $A$ of the equilateral triangle is 36$\sqrt{3}$

Geometry

Catherine R.

Megan C.

Maria G.

Kristen K.

(A few) Circle Theorems

Angles and Cirlce Theorems with chords and tangents

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

Catherine R.

Megan C.

Maria G.

Kristen K.

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

Geometry