Area of kites

what is the area of this figure and this figure right over here is sometimes called a kite for obvious reasons if you tied some string here you might want to fly it at the beach and another way to think about what a kite is it's a quadrilateral that is that is that is symmetric around a line that is symmetric around a diagonal so this right over here is a diagonal of this quadrilateral and it's symmetric around it this top part and this bottom part are mirror images and I think about how we might find the area of it given that we've been given essentially the width of this kite and we've also been given the height of this kite or if you view this as a sideways kite you could view this as the height and that the eight centimeters as the width given that we've got those dimensions how can we actually figure out its area so to do that let me actually copy and paste half of the kite so this is the bottom half of the kite and then let's take the top half of the kite so let's take the top half of the kite and split it up into sections so I have this little red section here I have this red section here and actually I'm going to try to color the I'm going to try to color the actual the actual lines here so that we can keep track of those as well so I'll make this line green and I'll make this line purple so imagine taking this little triangle right over here and actually let me do let me do this one too in blue so this one over here is blue you get the picture and try to color it in at least reasonably so color it in and then I could make I could make this line this segment right over here I am going to make orange so let's start focusing on this red triangle here imagine imagine flipping it over so imagine flipping it over and then moving it down here so what would it look like well then the green side is going to now be over here this kind of move colored side is still on the bottom and my red triangle is going to look something like this my red triangle is going to look like that now let's do the same thing with this bigger blue triangle let's flip it over and then move it down here so this green side since we flipped it is now over here and this orange side is now over here is now over here and we have our and we have we have this blue right over here and the reason that we know that it definitely fits is the fact that it is symmetric around this diagonal that this length right over here is equivalent to this length right over here that's why it fits perfectly like this now this is what we just constructed is clearly a rectangle a rectangle that is 14 centimeters wide 14 centimeters wide and not 8 centimeters high it's half of 8 centimeters high so it's 8 centimeters times 1/2 or 4 centimeters high and we know how to find the area of this this is 4 centimeters times 14 centimeters so the area is equal to 4 centimeters times 14 centimeters which is equal to let's see that's 40 plus 16 56 square centimeters so if you're taking the area of a kite you're really just taking 1/2 the width times the height or 1/2 the width times the height anyway you want to think about it