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1.4 Notes

Added Sep 03, 2015 •

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okay guys section 1.4 is perimeter and area on a coordinate plane you know what perimeter and area are you've done it many times it's just finding it on a coordinate plane so we may be using that distance formula to help us find the sites that remember if a line is horizontal or vertical you can just count but if it's a you're going to have to use that distance formula review first of all polygons do you remember what that is a polygon is a closed figure made up made three or more line segments and those are your sides it's a try a square rectangle an octagon anything like that or concave if you remember this I'm sure you've been taught that concave is caved in somewhere but the technical definition for convex and concave convet if you draw a line through all the sides right here none of them will go on the inside of the however if you draw one on concave see if I extend this side it goes inside the figure that's what my concave but you can also remember that a concave one caves in somewhere so if you extend all the sides if none of them go through the interior it's convex if one of the sides extends through the interior it's concave also you should tell all your names for all the sides for the number of sides of the polygon now remember any three sided figure is a try 44 sided figure is a quadrilateral which is a square a rectangle a trapezoid anything with four sides as a quadrilateral if it has five sides it's a pentagon  if it has six fix a hexagon  if it has seven now this is the one that you might have forgotten but if it has 7 it's heptagon  eight you should know that one octagon 9 is a nonagon clear is a decagon 12 is a dodecagon and then any other number besides those we just do end gone so if it's 15 it's 15 agon if it's 80 it'll be 80 or gone if it's 22 it'll be 22 a gun okay so if you don't have these memorized yet you need to memorize each one of these you need to know that is seven sided polygon is a heptagon you need to know that a 12-sided polygon is a dodecagon and you need to be able to identify them you also need to be able to tell me if they are convex or concave okay so on the bottom it just kind of gives you a paragraph form everything you need to know so if you'll look in geometry of figure that lies in a plane is called a plane figure all of these here's that you can draw are going to lie in a plane now polygons are closed plane figure formed by three or more line segments called sides you need to know what the odds are so each one of these line segments is your side okay now all the sides will always be line segments then it says each side intersects exactly two sides wanted each vertex so just like her angle we're going to have our vertex so this point right here D that's our vertex now we have several vertex Each corner is a verb okay then it says so that no two sides with a common vertex are collinear that means this sudden this side I'll be collinear would just be one big side you can name a polygon by listing the vertices in consecutive order okay now that's very important polygon ABCDE It Starts Here a and it goes a b c d e does it matter which vertex you start at but you need to pick me up and go in order around it and it doesn't matter if it's clockwise or counterclockwise I could also name this dcba it started see and go see dead any of those will work as long as you pick one and go in a certain order  they also you need to remember what perimeter and area are you should know this but perimeter is just the distance round  an object so it's just the distance around the outside Maria is the amount  of space inside and object now the other thing you need to know is the difference in how they're measured perimeter is single unit be measured in feet yards centimeters Etc area however is measured in square where are unit so it's answer will always be in feet squared yard squared centimeters squared and so on examples of what you're going to do in your homework so look at it number 1 through 4 classify the polygons by the number of side tell whether it is convex or concave now  count the number sides 1 2 3 4 5 if it has 5 sides it's up too gone  and is it concave or convex it is concave because it caves in right there if I extended this side it would go through the figure number to we have one two three four five six seven eight that isn't octagon and it is convex because if you extend all the sides none of them will go interior of the figure number 3 we have 1 2 3 4 5 6 7 again so that is an octagon as well but it is Khan Haze because it skin right here extended that Flyknit would go inside the figure Randomness last one let's see how many sides it has 1/2 play four five six seven eight nine 10 11 12 so that is a dodecagon and it is convex cuz nowhere does it cave in okay in exercises 5 through 8 find the perimeter end area you need to find both of the polygon with the given vertices so the first thing you want to do is pop the points that you are given so make an X and A Y axis first of all  and then plot your point x is24 so go over to and up one do 3/4 put a. Label it X okay why is zero so don't go left or right but go down to and that is your why NZ is positive to negative 2 so go down to their zorzi now those dots  so won't you connect the dots you're going to see that this line is straight up and down this line is straight across but this is a diagonal now if we want to find perimeter we need to know the distance of all three sides so if you count this since it's vertical you can just count 1 2 3 4 5 6 so we know that the sudden six across the bottom we can count one to so the bottom is too now what we don't know is this diagonal now the reason the only way that you can find that distance a diagonal on the coordinate plane is to use the distance formula so the distance formula is D equals the square root of X2 - X1 squared + Y2 - y1 squared so remember take the your point so we're going to find the distance between X and Y so here's my ex point and here's my wife point so remember subtract the Nexus 0-2 is negative 2 squared is 4 plus subtract the wise negative 2 minus negative -4 would be negative 6 squared is 36 so when you add those two together 36 and for you get 40 and the square root of 40 is 6.3 so this is 6.3 okay so to find the perimeter you add all of these sides together so that perimeter that one is going to be 6 + 2 + 6.3  and you get when you add those 14.3 not doesn't have any units so we'll just leave it like that now area how do you find the air of a triangle look on your formula chart on the area section and fun triangle you'll see that the area of a triangle is one half the base times the height now the big you need to know here is that the base and the height always have to be perpendicular to each other so here this is the height in this is the base because those would make a 90-degree angle right there so this is your height and this is your bait face so just get in so we get that the area equals 1/2  the base is 2 times the height is 6 so that half 2-ton sixes 12 1/2 of 12 is 6 so the area here is 6 the number 6 right here I'll let you do that on your own if you have questions you can ask me later let's skip down the number seven now now there's four points how many sides should that have if we have four points 3 points gave us three sides so four-point should give us Forsyth so this should be some kind of square rectangle or parallelogram or something like that so first thing you need to do is dry your axyz once you X & Y axis drawn start label in your points Jay is -4 one so one two score in up one that is Jay Kay is -4 negative 2  make sure you label it El is 6 positive 6 to go 6 this way in the negative to go down to so 1 2 3 4 5 6 down unto  lettuce ln6 RM is 6 positive one so what shape does that make connect your what's  so we have a rectangle no on a rectangle everything is horizontal and vertical so you don't have to do the distance formula cuz you have no diagonals just count so count each side this would be one to three so this side would be 3 and the side would be one two three four five six seven eight nine ten so this side would be 10 so the perimeter would be 10 + 10 + 3 + 3 side that's 26 so your perimeters 26 that how do you find the area of a rectangle look on your formula chart find area rectangle it's length times width or it can be base times height either one so that would be 10 times 3 which is 30 so number 8 is pretty much just like that you can do that one on your own  down the back for the last page 9 through team we're going to use this diagram over here so look at this diagram over here do you see a triangle right here and then a triangle right here okay both of those triangles and then if you look at them all together there's one two three four the outside is a four sided quadrilateral it's not a square it's not rectangle but it has four sides but number 9 says find the perimeter of triangle ABD so here's a there's B there's day so it's this tribal we need to find the printer first thing you need to do is find the length of every side so if we look on this side from a tabby that's one two 345 so this is 5 from B to d 1 2 3 4 5 6 now this has a diagonal so we're going to have to use the distance formula to find a daddy  okay so we'll find the distance formula Sadie down here no remember use your distance formula subtract your ex's first so I have to and I have negative for that makes -6 negative 6 squared is 36 + Nelson tractor wise 4 + -1 4 - -1 is 4 + 1 so that's 5 squared is 25 now add those together can you get the square root of 61 and the square root of 61 will round to 7.8 so this is 7 point so the perimeter here would be 6 + 5 + 7.8 so when you add those together you get hate .8 to the perimeter of the truck triangle is 18.8 now find the perimeter of BCD so BC Indie what we know this site is six but we've got to find this side so we need to plug that into the distance formula so again do BC  down here so square root okay we need to subtract the exes 2 minus negative one becomes plus one so two plus one is 3 3 squared is 9 +  subtract the wise beautiful one minus negative five so negative one minus -5 becomes plus so that is -1 and 5 make 4 Foursquare it is 16 when you add those together you get 25 + √ 25 is 5 so the spot now do the same thing for DC and you're going to see that DC is going to be the same as BC because if you look at it real quick negative four minus a negative one becomes plus one so negative before and one is 3 squared as 9 and then negative one minus negative five becomes negative one plus 5 same thing we just had right here or four squared is 16 so you're going to get 5 over here as well and now we can add our perimeter so we have five plus five 6 so we get 16 is the perimeter of this one it says fun perimeter ABCD song ABCD so it's the outside of the four sided figure so that's five five 5 and 7.8 so the perimeter would equal 5 + 5 + 7.8 which is 17.8 for your parameter there okay number 12 says find the area of triangle Abe So ABD is this one so we need Mason Ohio remember they have to make a right angle the base in the height have to be perpendicular so this would be your height in this would be your base so we're going to do make an 6 so if we look down here will do that area equals one half base times height so 1/2 5 x 6 so that equals 1/2 V * 6 is 30 1/2 of 30 is 15 the 13 we want to find the area of BCD so let's go back up here to BCD and look at it BCD if we don't have two sides that are perpendicular to each other but if you look at this triangle upside down this would be your height here and it would be perpendicular to this base right here that would be 90 degrees when we know this is 6 so count this one so that would be one two three four four would be on a hike so 6 and 4 is my base in my right so go back and look at this one and you'll do area equals 1/2 4 x 6 so that's 1/2 4 * 6 is 24/2 of 24 is  12 so that would be your answer there the last question says find the area of the quadrilateral this what's not a square it's not a rectangle side of trapezoid you don't have a formula for it down there now do you do when you don't have a formula for a shake your break it up into shapes that you know well we already have the area of this triangle and we they have the area this triangle so the area of this quadrilateral would just be this triangle plus this triangle added together in that gives you the whole thing so if you go down can you use these two formulas or these two areas 15 was one of them in 12 was one of them so the area of that quad lateral is just those two added together so 15 + 12 is 27 so the quadrilateral would be 27 okay I know that was all kind of quick but if you have any questions on any of this just come see me in advisory on Tuesday morning remember we don't have school Monday and a so over it and we'll go over it a little bit and clasp none of this should be too rough with just area and perimeter your homework is out of the book The Substitute will tell you what it is

Uploaded by Pam Chastain.

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1.4 Notes

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