About this video
The video finds the area of a kite that is 14 cm wide and 8 cm high. It cuts the top half into triangles, flips them and moves them below the bottom half to build a rectangle 14 cm wide and 4 cm high. The area is 4 x 14 = 56 square centimetres, so a kite's area is 1/2 the width times the height.
You'll be able to
- describe a kite as a quadrilateral that is symmetric around a diagonal.
- explain how a kite can be rearranged into a rectangle with half its height.
- find the area of a kite using 1/2 x width x height.
Key words
- kite
- A quadrilateral that is symmetric around one of its diagonals, shaped like a kite you fly.
- quadrilateral
- A flat shape with four straight sides.
- diagonal
- A line joining two corners of a shape that are not next to each other.
- symmetric
- Having two halves that are mirror images of each other.
- rectangle
- A four-sided shape with four right angles; its area is width times height.
Transcript
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 symmetric around a diagonal.
So this right over here is the diagonal of this quadrilateral. And it's symmetric around it. This top part and this bottom part are mirror images. And to 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 is 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 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 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 this one too in blue.
So this one over here is blue. You get the picture. Let me try to color it in at least reasonably. So I'll color it in. And then I could make this segment right over here, I'm going to make orange. So let's start focusing on this red triangle here. 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 mauve 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've flipped it, is now over here. And this orange side is now over here. And 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, what we just constructed is clearly a rectangle, a rectangle that is 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, any way you want to think about it.
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