Video Transcript
Perimeters of Rectangles with the
Same Area
In this video, we will learn how to
find the perimeter of rectangles which have the same area.
Meet farmer Jane. This is her farm. She measures each of her plots in
meters. This is her cabbage patch. If each of the squares measures one
meter by one meter, then her cabbage patch must measure four meters by four
meters. Let’s help farmer Jane work out the
area of her cabbage patch. We can think of her cabbage patch a
little bit like an array. There are four rows of four. If we multiply four meters by four
meters, that will tell us the area. We know that four times four is
16. The unit of measurement is
meters. And when we write area, we write
the units as meters squared or centimeters squared. So the area of farmer Jane’s
cabbage patch is 16 meters squared.
Jane is trying to work out how much
fencing she needs to put around her cabbage patch. We know that one side of her
cabbage patch measures four meters. In fact, all the sides measure four
meters. To help farmer Jane work out how
much fencing she needs, she needs to calculate the perimeter, which is the distance
all the way around the outside of her cabbage patch. So to calculate the perimeter, she
needs to add four meters plus four meters plus four meters plus four meters. So the perimeter of her cabbage
patch is also 16 meters. So farmer Jane thinks that the area
of a shape is the same as the perimeter. Is she correct?
So we already know that the area of
her cabbage patch is 16 meters squared and the perimeter of her cabbage patch is 16
meters. Farmer Jane has put her cows to
pasture. If each of the squares measures one
meter in length, then the length of her cow field is eight meters and the width is
two meters. To calculate the area of her cow
field, we need to multiply eight by two. Eight times two or two times eight
equals 16, so the area of the cow field is 16 meters square.
Let’s work out the perimeter. We know the perimeter is the
distance all the way around the outside of her field. To calculate the perimeter, we need
to add eight plus eight plus two plus two meters. Double eight is 16; double two is
four. 16 plus four equals 20 meters. Looks like farmer Jane was
wrong. The areas of these two shapes are
the same. They’re both 16 meters squared, but
each shape has a different perimeter.
So we’ve learned that the area of
two shapes can be equal, but they can have different perimeters. Can you think of another way to
draw a shape with an area of 16 meters squared? We know that eight times two is 16
and four times four is 16. 16 times one is also 16. So the area of farmer Jane’s
chicken run is also 16 meters square. What would the perimeter of her
chicken run be? To calculate the perimeter, we need
to add 16 meters and 16 meters plus one meter plus one meter. We know that double 16 equals 32
and double one equals two. 32 meters plus two meters equals 34
meters. So although farmer Jane’s three
fields have the same area, 16 meters squared, each field has a different
perimeter.
So we’ve learned that shapes can
have the same area but a different perimeter. Let’s put into practice what we’ve
learned by answering some questions now.
Here are two rectangles with the
same area. Which of them has the largest
perimeter?
In this question, we’re being asked
to compare the perimeter of two shapes which have the same area. Let’s calculate the perimeter of
our first shape. Perimeter is the distance around
the shape. To calculate perimeter, we need to
add together the length of all the sides. We can use the squares to help
us. The shape is two centimeters wide
and eight centimeters long. So to calculate the perimeter of
this shape, we need to add together eight plus eight plus two plus two
centimeters. Two lots of eight or double eight
is 16 and double two is four. 16 plus four is 20, so the
perimeter of our first shape is 20 centimeters.
The second shape measures three
centimeters by four centimeters. So to calculate the perimeter, we
need to add three centimeters plus three centimeters plus four centimeters plus four
centimeters. We know that double three is six
and double four is eight. Six plus eight gives us a perimeter
of 14 centimeters. 20 is greater than 14. So this is the rectangle with the
largest perimeter.
Michael and Mason are running
around playgrounds A and B, respectively, as shown here. The area of playground A equals
what unit squares. The area of playground B equals
what unit squares. Which playground has the larger
perimeter? And who will have run more after
the first round for both of them?
In this question, we’re comparing
the area and perimeter of two playgrounds. Let’s calculate the area of
playground A, and we’re asked to do this in unit squares. The length of playground A is six
unit squares and the width is four unit squares. So to calculate the area, we need
to multiply six by four. Six times four or four times six is
24. So the area of playground A equals
24 unit squares. Let’s calculate the area of
playground B. This playground is eight unit
squares long by three unit squares. So to calculate the area, we need
to multiply eight lots of three. Eight times three or three times
eight is also 24. The area of both playgrounds is the
same. The area of playground A equals 24
unit squares and the area of playground B is also 24 unit squares.
Now that we’ve calculated the area
of each playground, we need to calculate the perimeter of each playground. A perimeter is the distance all the
way around the outside edge of the playground. So to calculate the perimeter of
playground A, we need to add together two lots of six and two lots of four. Six plus six is 12, four plus four
is eight, and 12 plus eight equals 20. The perimeter of playground A is 20
unit squares. To calculate the perimeter of
playground B, we need to add together our two lots of eight and two lots of
three. We know that double eight is 16;
double three is six. 16 plus six is 22. 22 is greater than 20. So the playground with the larger
perimeter is playground B.
Now we can answer the final
question, who will have run more after they’ve completed a round of the
playground? In other words, if Michael and
Mason run all the away around the perimeter of their respective playgrounds, who
will have run the most? Since the perimeter of playground B
is the larger perimeter, the person who will have run the most is Mason.
What have we learned in this
video? We’ve learned that rectangles with
the same area can have different perimeters.
