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# Area of quadrilateral with 2 parallel sides

CCSS.Math:

Find the area of a US trapezoid by decomposing it into two triangles with parallel bases. Created by Sal Khan.

## Want to join the conversation?

- it would have been much faster is he just did 8*5=40/2 which equals 20 and then 4*5=20/2 whish is 10 then add them which is 30(6 votes)
- Would the formula 1/2x(b1 + b2)h work for composite figures(3 votes)
- Yep, since it is a trapezoid figure. :)(3 votes)

- why the height for second triangle is 5 :/(1 vote)
- The height is perpendicular to the base, so you would have to extend the line segment of the base which is 4 at least to the point of vertex on top left. Then the same 5 on bottom would be the perpendicular distance to this vertex. Think of the two bases as being parallel, distance between them will remain constant.(4 votes)

- why is the height 5?(2 votes)
- A wall is 12 feet long and 8 feet tall. There is a square window 4 feet long in the wall. What is the area of the wall surface?(1 vote)
- could I just have re-arranged the shape instead of doing the complicated thing that Sal was doing?(1 vote)
- water

water water water(1 vote) - I wonder how people can do this so quickly while I'm suffering in my own personal he!! lol.(0 votes)
- only vote for those who answer right and ask(0 votes)
- what is the formula to find the area of a triangle(0 votes)
- A= 1/2 base x height bh(2 votes)

## Video transcript

- [Instructor] What we're going
to try to do in this video is find the area of this figure. And we can see it's a quadrilateral. It has 1, 2, 3, 4 sides. And we know that this side and this side that they're parallel to each other. You can see that they
both form right angles with this dotted line. So pause this video and see
if you can find the area. All right. Now, if you had a little
bit of trouble with that I'll give you a hint. What if we were to take this quadrilateral and divide it into two triangles? So let me do this in a color
that you are likely to see. So if I were to draw a line like this it now divides the quadrilateral
into two triangles. If I were to take this
triangle right over here I could take it out and reorient it, so it looks something like this, where the base has length 8, and then the height right
over here, the height this has length 5. So that would be that triangle. And then, this triangle over here if you were to take it out
and reorient it a little bit it could look like this, where the base is 4, and the triangle looks something like, looks something like this. So the base is 4, and then the height is going to be 5. So this height right
over here, this height, we notice this is a right angle. So from here to here,
which is the same thing as from here to right over here, we know that this is 5. So that's my fairly big hint to you, if you know how to find
the area of a triangle. The area of a triangle we
know is 1/2 base times height. So the area of this one right over here is gonna be 1/2 times 8 times 5. And the area of this one over here is going to be 1/2 times the base, which is 4 times the height, which is 5. And we could evaluate each of these, or we could just add them together. That the area of the entire thing is going to be 1/2 times
this base right over here which is 8, times the height, which is 5, plus 1/2 times this side, you could do that as
the other base, times 4 times that same height, times 5. And obviously, you
could just evaluate this or we could see some
interesting things about it. We could express this as well if we were to factor
out 1/2 and the 5 here. This could be rewritten as 1/2, 1/2 times 8 plus 4, 8 plus 4. And then, all of that, all of
that times 5 right over here. And so, another way you
could think about it is the average of the length
of these two bases. You could view this as base 1 and base 2, you multiply that times the height and you have the area
of this quadrilateral. Well, what's that going to be? 8 plus 4 is 12. 1/2 times 12, this is all going to be 6. 6 times 5 is going to be
equal to 30 square units. You could have figured it out here too. 1/2 times 8 is 4, times 5 is 20. And then, this would've
been 1/2 times 4 is 2, times 5 is 10. 20 plus 10 is 30 square units once again.