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

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

Geometry

Chapter 11

Areas of Plane Figures

Section 4

Areas of Regular Polygons

Polygons

Surface Area

Circles

Missouri State University

Piedmont College

University of Michigan - Ann Arbor

Lectures

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electoral triangle that's inscribed in a circle. And I've just added some extra notation to the diagram. So the O it'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'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's three is If you imagine the line all the radius circled, it would make three triangles. So will be these angles here. That's the PXs one that on there. So compared to that. So this is the pay accessible and that's 120 degrees. So we know that the angle, it's gonna be half of that. You can see where it split, where it goes to the app within their but that line, that's kind of 100 20 over to. We're just gonna ankle 68 degrees. So then we can use the angle. Oh, because we know that there's 180 degrees in the triangle. So you want 80 minus that, right? And real 90 But 60 Grady'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's every red. Well, some you, uh, so that'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's gonna come out 2 to 3. We do the same acts. Will be sign ex something. Ah. Oh, but there's And at six, this isn'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's not just shape. Why, That is a diagram. This is excess. And we noticed that they are is the mid plane. So it's gonna be to those that'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.

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