Video: Area: Whole and Half Squares

In this video, we will learn how to measure the areas of shapes drawn on grids with whole and half squares by counting and matching halves.

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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.