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Studying for a test? Prepare with these 5 lessons on Module 7: Geometry and measurement word problems.

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# Comparing areas and perimeters of rectangles

Video transcript

So I have this yellow
rectangle here, and we know two things
about this yellow rectangle. We know that it
has a length of 10, that the length of this
side right over here is 10. And we also know that
this yellow rectangle has an area of 60
square units, whatever units we're
measuring this 10 in. So what I want you to do
is now pause this video, and based on the
information given on these other rectangles--
so in some of them we give you two of their
dimensions, in some of them we give you something
like the perimeter and one of the dimensions--
I want you to pause the video and think about which of these
rectangles, if any of them, have either the same area
or the same perimeter as this yellow rectangle. So pause the video right now. Well, the best way to
figure out which of these have the same area or perimeter
as this original yellow rectangle is to just figure
out the area and the perimeter for all of these rectangles
and see which ones of them are equivalent. So we already know
the area for this one, but we don't know its perimeter. So how do we figure that out? Well, to figure
out perimeter, we would need to know the
lengths of all the sides. Well, if the area is 60 square
units, that means the length times the width is equal to
60, that 10 times this width right over here is
going to be equal to 60. So 10 times what is equal to 60? Well, 10 times 6 is equal to 60. 10 times 6 is equal
to 60 square units. 10 units times 6 units is
equal to 60 square units. Fair enough. So how do we figure
out the perimeter now? Well, this is a rectangle. So we know if this
length is 10, then this length must also be 10. And if this width is 6, then
this width must be 6 as well. And now we can figure
out the perimeter. It's 10 plus 10 plus
6 plus 6, which is 32. So let me write that down. The perimeter of our
original yellow rectangle is equal to 32. Now let's go on to each
of these other rectangles and figure out what their
perimeters and the areas are. We already know the perimeter
for this purple or mauve rectangle, but we need
to figure out its area. In order to figure out
its area, we can't just rely on this one dimension
just on its width. We have to figure out
its length as well. So how do we figure that out? Well, one way to realize
it is that the perimeter is the distance all the
way around the rectangle. So what would be the distance
halfway around the rectangle? So let me see if I can draw it. What would be the distance
of this side, our length, plus this side? Well, it would be
half the perimeter. 5 plus something is going to
be equal to half the perimeter. Remember, the perimeter
is all four sides. If we just took these
two sides, which would be half the perimeter. So, these two sides
must be equal to, when you take their sum,
must be equal to 17, half the perimeter. So 5 plus what is equal to 17? 5 plus this question
mark is equal to 17. Well, 5 plus 12 is equal to 17. And you can verify this. 12 plus 5 is 17, and
then that times 2 gets us the perimeter of 34. Now, given that, what is
the area of this figure? Well, the area's going to
be 12 units times 5 units to get 60 square units. Area is equal to 60. So this one right over
here has the same area, different perimeter. Same area as the original yellow
rectangle, different area. Now let's go over here. So this is not just a rectangle. This is also a
square, because I have the same length
and the same width. So what's the area here? Well, for the area, I
just have to multiply the length times the width. 8 units times 8 units
is 64 square units. And what is the perimeter here? Well, these two sides are going
to make up half the perimeter. If I wanted to figure
out the whole one, I know this is also
8 and this is also 8. So the perimeter is 8 times 4. 8 times 4 sides,
which is equal to 32. So this square right over
here has a different area, but it has the same perimeter
as our original yellow square. Now let's move
onto this blue one. What's the area? And you're probably
getting used to this. 15 units times 4 units is
going to be 60 square units. And what's the perimeter? What's the perimeter? Well, it's going
to be 4 plus 15, and whatever that is times 2. 4 plus 15 is 19. And then 19 times 2 is 38. So this one right here
has the same area, different perimeter
as our original. Now, finally, here in
purple, what is the area? The area is 10 times 20,
which is equal to 200. So if it's 10, say, well,
10 units times 20 units is 200 square units. And what is the perimeter? What is the perimeter? Well, 10 plus 20 is 30, but
I've just considered only two of the sides right here. That's only half way around. So 10 plus 20 is
30 times 2 is 60. So let's see. This has a different
area, and it also has a different perimeter. This one's perimeter looks
just like the same number. It's 60, as is the
area here, but that's not what we're comparing. We have a different
perimeter and different area. So neither of these are the
same as our original rectangle.