Video Transcript
Rectangle A and rectangle B have
the same perimeter. Which of them has a larger
area?
In the pictures underneath this
question, we can see two rectangles. These are labeled rectangle A and
rectangle B. Now, just by looking at these
rectangles, we can see that they’re slightly different sizes. But there’s something the same
about them. We’re told in the first sentence
that both rectangles have the same perimeter. Now we know that the perimeter of
the shape is the distance all around it. So this first sentence tells us
that the distance around both rectangles, although they look slightly different, is
the same.
The length of rectangle A is seven
centimeters. We can see this because it’s
labeled seven centimeters. But also if we count the squares,
we can see it’s seven squares long. Each square must be one centimeter
long. So rectangle A is made up of two of
these longer sides worth seven centimeters, and two lots of seven is 14. And then the width of this
rectangle is two centimeters and there are two sides that are worth this amount. So two lots of two equals four. And if we add 14 and four together,
we can see that the perimeter of rectangle A is 18 centimeters.
And if we quickly look at rectangle
B, we can see that the same is true. It has two sides with a length of
six centimeters. This is 12 centimeters
altogether. But the width of the rectangle is
three centimeters, so two sides are worth three centimeters, and three doubled is
six. So if we add all the sides
together, 12 and six equals 18 again. Rectangle A and rectangle B have
the same perimeter. But which of them has a larger
area? We know that the area of a shape is
the space inside it. And we can find the area of both of
these rectangles by counting the squares inside them.
We can see that rectangle A is made
up of two rows of seven squares. It has an area of 14 square
centimeters. In other words, 14 square
centimeters fit inside it. Now, if we look at rectangle B, we
can see it’s made up of three rows, and each row contains six squares. And three times six is 18. The area of this rectangle is 18
square centimeters. 18 square centimeters fit inside
it. And this tells us something really
interesting about shapes. They can have the same perimeter,
but they don’t have to have the same area. Both rectangles have the same
distance around them, but they don’t have the same space inside them. 18 square centimeters is greater
than 14 square centimeters, so the rectangle with a larger area is rectangle B.
