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Video Notes #11.1-11.3 for Geometry

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all right and hello students and welcome to your video notes this is a continuation of notes for Section 11.1 through 11.3 this is for our geometry class I believe we left off by talking about winners last time so we have three items to talk about today prisons 103 items silver prisms about what day are we certain talk about the definition and how they are polyhedrons with parallel bases they have congruent and parallel all polygons somewhere in the figure L A of course remember stands for lateral area essay stands for surface area lateral area means the area all the way around the actual dimensional figure but you don't include the bases surface area and lateral area of one of the bases anymore High Times to hike or altitude service area area calculated here and you add the base area x 2 because there are two bases one of the top or the bottom two formulas for let's go ahead and move on to a circle an oval so go ahead to start Put It Center and and place another. From this. the top of the Scoville go ahead and connect your lateral side of this cone and there's your three-dimensional figure we're going to go ahead and I'm going to call her add a triangle right in the middle check this out from the top I'm going to drive dash line straight down towards the center then I'm going to draw a radius like that towards Circle noticed that this is a right angle so you have a right triangle in the middle of your figure in tennis label the radius it is of course our for radius the heights right so you can label at age for height but was interesting about a cone is that we are not that we don't necessarily we actually don't look at the height here go ahead and highlight the edge here this Edge which I'm going to highlight orange color code in Orange is what need it. Lynx is what they called the lateral height and that is what is used to calculate the area of a cone K and of course the lateral height is also the hypotenuse of this triangle that sits in this right triangle that it's in the middle of the cone also noticed that if you were to take this right triangle that sits in the middle of a 360 degrees right thigh pain we cover the entire area or the entire lateral area of a circle as the base at the bottom so it starts by drawing a circle with a C enter in the lateral area of a cone is actually a circle tangent to the circle what would be the equivalent of a piece pizza slice missing from its and that would be the this angle right here call Sada and I will teach you how to calculate that angle in another set of notes but not today but that's what it looks like an important fact about the cone is the height of the cone depends on the radius so be aware that come back to this fact it's very important and here are your two formulas lateral area is 1/2 * 2 base circumference of the lateral surface area is the lateral area plus the base area I hear the bay circumference right to Pi R 2 and a 1/2 actually cancel out so you'll often see the lateral area of a cone being referenced as Pi * R * the lateral height cuz they won't have fun. cancel each other out the last piece is not that one. All right what does it look like look like really many things you can have a rectangular base square base you can have a lot of different faces an example of start off with a square based pyramid which is the more typical on horse the square base we do know if I drawing a shape that looks more like a parallelogram where to find the center I put my pencil right above that Center and I'm going to move my pants straight up and that is my going to go and drop sides the front with solid lines but a dash line to the back end and this front there we go I'm going to go ahead and again I can see it before with the cone I'm going to drop altitude in the center what's the temperature on the top to the center of the Bay and I'm going to draw a I guess what would be a nap with them on that bay Square notice that I have a right angle there and noticed that we have another right triangle now on the face the pyramid here I'm going to connect the top to this Edge can you see that right triangle in the middle of the pyramid that's important okay so the eight here would be that would be the opposite right or half of the side lengths this will be the height right but we're not going to use the height because again for the pyramid we're going to take a look this is right here. Edge of course just like in the cone is the lateral height and again notice at the lateral height is the hypotenuse of Skinner try right triangle the lateral Heights is a hypotenuse of a right triangle inside of the pyramid sorry the words got mixed up simple you have a square the center and you have these triangles it came out from each side that's an easy one let's take a look at the formulas and we'll be done with her notes lateral area is 1/2 find the base perimeter comes to lateral height as the lateral area plus the base area of course we only have one facing area all right I hope that helps

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Video Notes #11.1-11.3 for Geometry

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