6 th grade Polygons on the coordinate plane

okay so let's go ahead and get started today we are doing polygons on the coordinate plane our learning goal is that students will be able to plot points on the coordinate plane and find the area and perimeter of the figure if you need to pause this video at any time to slow things down or write things down please do so remember to find area to find area of parallelograms or rectangles or squares we multiply the base times the height to find the area of triangles which is three-sided shape we multiply the base times the height and then divide it by two to find perimeter that's just adding up all of the sides together so whether it's triangle we would add up all three sides together if it was square we would add all four sides together okay so for perimeter we're just adding them all up together okay sorry if you needed to pause this to write this down that's good idea okay so we are finding the area and perimeter of this figure so the first thing we need to do is graph the figure so this is all in quadrant one by the way quadrant one it has it doesn't show all four quadrants here it just shows you quadrant one for this particular graph okay so is in coordinate or ordered pair one one so we go over to positive one up to positive one that's okay is positive one positive seven so we go over to positive one up to positive seven that's is positive five positive seven so we go to the right to positive five and then up to positive seven that's and then the last one is positive five positive one okay so this is our shape it is rectangle i'm terrible at drawing lines on this thing that was actually pretty good one okay okay so now we are finding the area in the perimeter so what like to do is like to do jumps think those are the easiest so from to we're gonna jump one two three and four from to one two three four five and six and then if this side is four this side's gonna be four and if this side is six this side is going to be six so remember for perimeter we're just adding all sides together so perimeter is so equals four plus six plus four plus six four plus six is ten so ten plus ten is 20. so 20 units is the perimeter to find the area since this is rectangle we are doing base times height anytime you see two letters next to each other that means we are multiplying them together so bh stands for base times height our base is four and then our height is six so four times six gives me 24 and it doesn't tell us what these units are it doesn't say that the units are inches or miles or feet it just says they're units right actually it doesn't say anything it's just on the coordinate plane or graph so anytime it doesn't tell you though and it's on graph you're just going to put units and then you're going to square those units because any time we're talking about area our answer is always squared so our two answers are this one and this one and notice what we learned yesterday with finding the distance between two points helped us here because we needed the distance between and to figure out what this side and this side were and we needed to figure out what the distance between and to figure out what side and is equal to so that is how the distance how learning the distance finding the distance between two coordinates helps us here make sure that all of this is written down before you move on with us okay number two we're gonna again graph these coordinates so is at 3 6 so we're going to go to positive 3 up to positive 6. is at 7 6. so we're going to go over to 7 up to positive 6 is at positive 7 positive 2 and is that positive 3 positive 2. so here is our shape looks like square to me but let's figure that out so from to one two three and four units from to one two three and four units so if this side is five then sorry if this side is four then the set is also four and if this side is 4 then this side is 4. if we are finding the perimeter we are adding all of our sides together so 4 plus 4 plus 4 plus 4 plus 4 is 8 plus 4 is 12 plus 4 is 16 so our perimeter is 16 units and then area again for square its base times height our base here is 4 and our height is also 4 so 4 times 4 and 4 times 4 also gives us 16. so our perimeter our perimeter and our area for this particular problem are both the same except for perimeter we use just units and for area we use units squared so it's 16 units squared for area and perimeter is just 16 units okay make sure you get all of this written down before moving on with us okay now this is parallelogram it's already given us the shape okay so parallelograms are little bit tricky well they're trickier than rectangles and squares at least we want to count from this point to this point okay you don't want to go as far over you just want to go to where the shaded area is okay from this point to this point you could also do it up here from this point to this point okay so one two three four and five and the bottom would be the same one two three four and five now we cannot count the sides here which is why we're only finding the area for this one because you cannot count diagonal side here you can't count this as like this is half square do you know what mean you can count the height but the way we count the height is from the bottom to the very top and it has to be right angle okay these are all slanted okay the ones on the very ends are slanted so we want to count this one straight up the middle so this will be our height so one two three four and five so our height is also five so if we're finding the area of parallelogram it's base times height and our base is 5 and our height is also 5. so 5 times 5 gives me 25 so our area is 25 units squared now sometimes like on fsa they may have the height be off to the side so it may look something like this it may have like dotted line out here to the side showing you that this is the height and they usually tell you so if they said that this was the height it was five centimeters or whatever they can write it off to the side for you sometimes they'll ask you to find the perimeter for shape like this but if they're asking you to find the perimeter they're going to need to tell you what these sides are equal to for example this is five this is five this is five and this is five or they would say this is six and this is six does that make sense if they're asking you this question wasn't asking you but if it was asking you to do the perimeter they would need to give you what at least one of the side links was equal to okay next one we are finding the area and perimeter of this figure i'm gonna outline this figure little better okay what would do for this one is break it down into two shapes and then add our answers together so would break it down here so now it looks like we've got rectangle and square so i'm going to do two areas and then add them both together so base times height and base times height so our base and our height for this bottom one our base is one two and our height is one two so area equals two times two and 2 times 2 gives me 4. so the area for this bottom one is 4 and here our base is can do it up top 1 2 3 four and five and our height is one two three four so our height our base is five and our height is four and the reason we didn't count this entire side for the area is that we broke it down into smaller shapes so we were finding just the area for this shape that's the five times four and then we were finding just the area of this shape that's the four times or sorry the two times two so five times four gives me 20 and we already did the two times two which gives me four and then we're just adding those together 20 plus four gives me 24 units squared and you should be able to you may not always be able to especially with parallelogram like we just did in the last problem but when we are given squares you should be able to count all of the squares and they should equal 24. so if we counted all of these in the middle here we should get 24. for example one two three four five if you keep keep if you kept doing this for the whole thing you should be able to get 24 squares so when you've got rectangles that's really easy to find the area because you can just count the squares but don't always rely on that you'll need to rely on the formulas base times height because in problems like our last one where we had this one is parallelogram know it's hard to see behind that our parallelogram we cannot just count the squares here because not all of the squares are filled this one is like just little bit squared or squared little bit filled so it's hard to say that's point three tenths filled we can't say that because we don't know for sure that it's exactly three tenths so always do base times height when it's parallelogram and usually for squares and rectangles that's going to be most beneficial as well okay so the area is 24 units squared i'm going to clear all of this so we can do the perimeter now so for perimeter we're just adding up all the sides together so one two three four one two three one two one two one two three four five six and one two three four five so we add all these together five plus six plus two goodness plus two plus three plus four five and six is eleven eleven plus two is thirteen thirteen plus two is fifteen fifteen plus three is eighteen and eighteen plus four gives us twenty two so our perimeter is 22 units remember units is never squared it's just units okay and last one we're just finding the area here because it's triangle so for area for triangle we need to do base times height and then divide it by two our base is one two three four five six and our height remember is from the bottom to the very top i'll do it in blue from the bottom to the very top and it has to be somewhere where it's it perpendicular to the bottom so right angle here so one two three and four so that's four okay so our denominator sorry our base is six and our height is four and then we'll divide by two in the end so six times four that gives me and then we still have to divide by two 24 divided by two is 12. so 12 units squared okay that's all have for you guys today hope you guys have fantastic day and will see you tomorrow