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# Perimeter & area of composite shapes

Sal finds perimeter and area of a non-standard polygon. Created by Sal Khan and Monterey Institute for Technology and Education.

Video transcript

Find the area and
perimeter of the polygon. So let's start with
the area first. So the area of this
polygon-- there's kind of two parts of this. First, you have this part
that's kind of rectangular, or it is rectangular,
this part right over here. And that area is
pretty straightforward. It's just going to
be base times height. So area's going to be 8 times
4 for the rectangular part. And then we have this
triangular part up here. So we have this area up here. And for a triangle, the area
is base times height times 1/2. And that actually
makes a lot of sense. Because if you just
multiplied base times height, you would get this entire area. You would get the area
of that entire rectangle. And you see that the triangle
is exactly 1/2 of it. If you took this
part of the triangle and you flipped it over,
you'd fill up that space. If you took this
part of the triangle and you flipped it over,
you'd fill up that space. So the triangle's area is
1/2 of the triangle's base times the triangle's height. So plus 1/2 times
the triangle's base, which is 8 inches, times
the triangle's height, which is 4 inches. And so let's just calculate it. This gives us 32
plus-- oh, sorry. That's not 8 times 4. I don't want to confuse you. The triangle's height is 3. 8 times 3, right there. That's the triangle's height. So once again, let's go
back and calculate it. So this is going to be 32
plus-- 1/2 times 8 is 4. 4 times 3 is 12. And so our area for our
shape is going to be 44. Now let's do the perimeter. The perimeter-- we just
have to figure out what's the sum of the sides. How long of a
fence would we have to build if we wanted to make
it around this shape, right along the sides of this shape? So the perimeter-- I'll
just write P for perimeter. It's going to be equal to 8 plus
4 plus 5 plus this 5, this edge right over here, plus--
I didn't write that down. So I have two 5's plus
this 4 right over here. So you have 8 plus 4 is 12. 12 plus 10-- well, I'll
just go one step at a time. 12 plus 5 is 17. 17 plus 5 is 22. 22 plus 4 is 26. So the perimeter is 26 inches. And let me get the
units right, too. Because over here, I'm
multiplying 8 inches by 4 inches. So you get square inches. 8 inches by 3 inches, so
you get square inches again. So this is going to
be square inches. So area is 44 square inches. Perimeter is 26 inches. And that makes
sense because this is a two-dimensional
measurement. It's measuring something
in two-dimensional space, so you get a
two-dimensional unit. This is a one-dimensional
measurement. It's only asking you,
essentially, how long would a string have to be to
go around this thing. And so that's why you get
one-dimensional units.