Video Transcript
Area, Whole, and Half Squares
In this video, we’re going to learn
how to measure the areas of shapes drawn on grids with whole and half squares by
counting and matching halves. How could we find the area of this
rectangle?
Area is the size of a surface or
the amount of space it covers. So the area of this rectangle is
the amount of space inside the pink lines. When we measure the area of a
shape, we measure it in square units. This is a square unit. So to find the area of this
rectangle, we just need to count the number of square units it covers. One, two, and another two makes
four, and four more makes eight. The area of this rectangle is eight
square units.
How could we find the area of this
cat shape?
Let’s start by counting the number
of squares the shape covers. Here are two squares, four,
six. Here’s a row of four squares. And we know that six and four is
10. Another row of four makes 14
squares. And another four makes 18, plus
three more gives us a total of 21 squares. We’ve counted all the squares. Now we need to count all of the
triangles. Did you notice that each triangle
is half of a square? If we were to put two of these
triangles together, it would make a whole square. So if we pair two triangles
together, we’ve got one square.
We can put these two triangles
together to make one square. We can pair these triangles
together to make another square. Here’s one more pair, giving us
another square. Here’s one more square. And we can put our last two halves
together to make another square. Let’s count how many whole squares
we’ve made from our triangles. One, two, three, four, five,
six. Now we can add to find the total
number of square units. 21 plus six is 27 square units. The area of the cat figure is 27
square units.
Now that we’ve learned how to find
the area of shapes with whole and half squares, let’s have a go at answering some
questions now.
Find the area of the shape.
In this question, we have to find
the area of the shape given. Area is the amount of space a shape
covers or the size of the shape’s surface. We can see that our shape has been
drawn onto a square grid. And we measure area in square
units. So to find the area of this shape,
we just need to count the number of square units it covers. Here are two square units, three,
four, five, six, seven, eight, nine, and three more squares makes 12.
But we haven’t counted all of the
squares that the shape covers. This rectangle is half a
square. If we were to place these two half
squares together, we’d make one complete square. One more than 12 is 13. And if we pair these two halves
together to make another square, we’ve got a total of 14 squares. We counted the number of complete
squares, and we put half squares together to make whole squares. The area of our shape is 14 square
units.
Find the area of this shape.
Area is the amount of space a shape
covers. We have to find the area of the
shape we’ve been given. We can think of the area as the
amount of space inside the blue lines. This shape has been drawn onto a
square grid, and we call each square a square unit. We measure area in square
units. So to find the area of our shape,
we just need to count the number of square units it covers.
But this isn’t a square. It’s a triangle. Here’s another triangle. Each of these triangles is worth
half a square. We can put two halves together to
make a whole square. So, so far, we’ve counted one
square unit. Now we can count the whole
squares. Our two halves make one whole
square, and there’s another three on the top row, which makes four. We’ve got four more on the second
row, which gives us a total of eight. Four more squares on the bottom row
makes a total of 12 square units. And we’ve got another triangle,
which we know is worth half a square. We counted a total of 12 and a half
square units. The area of this shape is 12 and a
half square units.
We counted the whole squares. We put the half squares together in
pairs to make more whole squares. Altogether, the shape covers an
area of 12 and a half square units.
Charlotte has drawn a shape with an
area of 12 square units. Which two shapes have an area that
is different from Charlotte’s shape?
Charlotte has drawn this shape. And we’re told her shape has an
area of 12 square units. So Charlotte’s shape covers 12
squares on the grid. This is how much space her shape
takes up. We’re shown another three shapes:
shape one, shape two, and shape three. We have to choose the two shapes
that have an area that is different from Charlotte’s shape. In other words, we have to find two
shapes that do not have an area of 12 square units.
To find the area of each shape, we
just need to count the number of square units it covers. Let’s start with shape one. Here’s two squares, and another
three makes five squares. Five and two more is seven, and one
more makes eight. Now we need to count the
triangles. Each of these triangles is half a
square. So if we put two halves together,
we’ll make one whole square. So if we put these two halves
together, we’ll have nine squares. These two halves make another whole
square, which makes 10. Two more halves makes 11
squares. And we’ve got a half left over. So the area of shape one is 11 and
a half square units.
We know that Charlotte’s shape has
an area of 12 square units. So we know that shape one has an
area which is different to Charlotte’s shape. Now we just need to find our second
shape. What’s the area of shape two? Let’s count the number of
squares. One plus three makes four, five,
six, seven. Two more than seven is nine. Another two makes 11. 12, 13, 14. So the area of shape two is 14
square units. This is the second shape that has
an area different from Charlotte’s shape, because the area of Charlotte’s shape is
12 square units. The two shapes that have an area
different from Charlotte’s shape are shape one and shape two.
What have we learned in this
video? We’ve learned how to find the area
of shapes with whole and half squares.
