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## Geometry (all content)

### Course: Geometry (all content) > Unit 7

Lesson 7: Area of trapezoids & composite figures# Area of kites

CCSS.Math:

To find the area of a kite, you need to know the lengths of the kite's two diagonals (the lines that cross through the middle of the kite). Multiply the lengths of the two diagonals together, and then divide by 2. This will give you the area of the kite. Created by Sal Khan.

## Want to join the conversation?

- at around3:37, sal says 56cm squared but puts the exponent 3 [A.K.A. cubed] when he should have put 2 [A.K.A. squared.](34 votes)
- why do we need to know this?(2 votes)
- I'll give you the short term answer and the long term answer.

Short term: So we can graduate school and get a good job. We need to know math in every grade, even in college.

Long term: Throughout our life, we will need to use math in many things. Say you build a mansion with the money that you made before retiring, and you need a kite shaped pool with a volume of 3000 cubic yards of water. Would you be willing to fork over more money to the builders to calculate something you could just do yourself?

Another example would be if you were hosting a large party, and you have a kite-shaped table for all of the food. If you put too much food on the table, it will spill over. So, you need to accurately calculate how much food you will be able to fit on the table before it overflows.

Hope this helps!(65 votes)

- Isn't a Kite and a Rhombus the exact same thing?(0 votes)
- A kite is a quadrilateral with two pairs of congruent sides that are adjacent to one another. They look like two isosceles triangles with congruent bases that have been placed base-to-base and are pointing opposite directions. The set of coordinates {(0, 1), (1, 0), (-1, 0), (0, -5)} is an example of the vertices of a kite. A rhombus is a quadrilateral with all four sides congruent. The more common shape name for a rhombus is "diamond". Since a rhombus also happens to have two pairs of congruent sides that are adjacent to one another, then it follows that a rhombus is also a kite. So, all rhombuses are kites, but not all kites are rhombuses.(29 votes)

- What if you don't have the measurement of the diagonal?(6 votes)
- A kite is just double of a triangle.Why not half the hight and use the formula for calculating triangle area without the multiplication by 1/2 as a kite is
**double**of a triangle?(3 votes)- It is not necessarily made up of two of the same triangle. Therefore you can’t just modify the formula for the area of a triangle. You have to find another formula.(3 votes)

- I got the same answer by finding the area of the triangle above, 28, and then multiplying by two (to reflect the area of the bottom triangle). Is this a good way to achieve the same result or is it better to try to convert the kite into a rectangle? Thank you.(1 vote)
- That works fine, you are basically doing the same thing as Sal, you are doing A = 1/2 bh *2, so 1/2*2=1 and you end up with just A = bh. The final idea for Sal is that the area of a kite is given by A = 1/2 d1*d2 where d1 is one diagonal and d2 is the other. Kites also have diagonals that are perpendicular to each other.(7 votes)

- I don't really understand the formula of kite

What is it??(2 votes)- Just like a rhombus, A = 1/2 d1*d2 where d1 and d2 are the two perpendicular diagonals of a kite.(4 votes)

- Do we still have to multiply by 2 the total of 56cm^2? or that's just it? 56cm^2?(3 votes)
- If you just find the area of half of the kite and multiply that by 2 you would get the answer right?(2 votes)
- Yes, if you find the area of half the kite, and subsequently multiply it by 2, you get the full area of the kite. For example:

A kite is 20 centimeters in length and 14 centimeters in height. If you find the area of half the kite, and then multiply it by 2, you get the area of the kite.(1 vote)

- why isn't there any exercise question for area of kites?(2 votes)
- there isn't a exercise because maybe it isn't common to find the area of a kite in the real world.(1 vote)

## Video 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.