 This video is called Find the Exact Area and Perimeter of the Parallelogram 2. So in this problem we are going to find perimeter of the parallelogram and area of the parallelogram. So again remember just perimeter is adding up all of the sides of the parallelogram and area the formula that we know is area is base times height where it's very important to remember that you pick the base and the height carefully they have to be perpendicular. Well let's start with perimeter I think we'll actually get this one done very quickly. If you can remember back in chapter six the properties of a parallelogram one of the properties is that opposite sides are congruent so if the top is twenty the bottom's twenty the right's thirty the left is thirty so the perimeter is simply going to be twenty plus thirty plus twenty plus thirty which gives us a hundred units. So that took care of that actually very quickly alright so then let's go ahead and look at area. Well area is base times height let's pick our base and pick our height. They have to be perpendicular so I don't think I want to pick this because I don't have a imaginary line to drop down. I could but it looks like they already did one for me. If we pick this as our base this dotted line that drew in could be considered our height because it's already marked as being perpendicular. So I think that is the route I'm going to take so I already have my base as thirty now I just need to spend some time finding the height that imaginary line and once I do that I'll be set. Well looking at that it's kind of hard to know what to do but oh school day is done it's kind of hard to know where to start so you have to really look and think about what you're given. We gave you a sixty degree angle down here in the bottom right of our parallelogram. Well another property of parallelograms was that opposite angles are congruent. So if the lower right is sixty the upper left is going to be sixty. I know I have a ninety degree angle here so I've got a special right triangle where if this is sixty this is ninety well then that must be thirty. I'm going to redraw this down here so we can orient it in a way that we're more familiar with where we've got the ninety we've got the sixty we've got the thirty and it looks like all we know is that this hypotenuse is twenty. So let's think about it which side am I caring about? Caring about this side because this is the height this is that dotted line right in the picture so hold on so once we can alright sorry about that so we're on our thirty sixty ninety we want to find the long leg the dotted line because that will be the height which is what we need for our formula so I remember opposite my thirty is n opposite my sixty is n root three opposite my ninety is two n so which side do we have something we can work with right here that hypotenuse is represented by two n and we're also told it's twenty so two n equals twenty so when you divide both sides by two we get n to be ten so that makes the short leg ten and the long leg ten root three sorry about this lots of announcements alright so on this picture it puts this little guy is ten that's as twenty and my imaginary line my height is ten root three so the height is the one I need is the ten root three so I'll put that into my formula the base was thirty the height was ten root three since it's multiplication we are allowed to combine these to be thirty times ten is three hundred so we have three hundred root three and we label our answer unit squared because we were finding area so the perimeter of this parallelogram is a hundred units the area is three hundred root three units squared