In today's video we're going to cover how you can find the area of strange looking shapes like these three. The problem with shapes like these is that they don't have their own formulas, like rectangles or triangles do, and so to find their areas we instead have to split them up into smaller shapes that we do know the formulas for. To quickly recap, the main formulas you need to know are these four here, which are the ones for rectangles, parallelograms, triangles, and trapeziums.
So when you're given a weird shape, the aim is to break it up into some combination of these four shapes that we know the formulas for. And one thing to point out is that we sometimes call these four easy shapes simple shapes, because we have formulas for them. Whereas the more complicated shapes that we're focusing on in this video are often called compound, or composite shapes, because they're made up of two or more simple shapes. Let's start with this one in the middle, and add some measurements so that we can work through it. The first thing to spot here is that if we draw a horizontal line across the top here, then we can split this shape into a rectangle at the bottom and a triangle at the top.
So then all we need to do is find the area of each of them and add the two together. So to find the area of this rectangle we need to use this formula in the top left, and do length times width. which in our case would be the length of 5cm times the width of 4cm, which gives us 20cm2.
Then to find the area of the triangle at the top, we need to use this formula of 1 half times base times height. The base will just be 5cm, because it's the same length as this base of the overall shape. However, we haven't actually been told the height of the triangle. So we're going to have to work that out for ourselves.
What we do know is that the height of the entire shape is 7cm, and the rectangle makes up 4cm of that. So the height of the triangle must just be the difference between 4cm and 7cm, which we can find by doing 7 minus 4 to get 3cm. And now that we have our dimensions, we can find the area by just doing one half times the base of 5 times the height of 3, and we'll get 7.5 square centimetres. And then to finish the question, we work out the total area of the shape by adding together the areas of our rectangle and our triangle.
So 20 plus 7.5, which is 27.5 square centimetres. And that's our answer. If you look at this next one, you can see that this bit at the top is sort of sticking out a bit, and so to make it easier for ourselves we can just cut that bit off with a horizontal line along here. And we're now left with a big rectangle at the bottom, and a small trapezium on top.
To find the area of the rectangle we just do a length times width again, so 15 times 12, which is 180 centimetres squared. Next, if you look at the formula for trapeziums in the bottom left, we first have to find the average length by doing a plus b over 2, and then multiply that by the height. And remember a and b in this formula are just the top and bottom lengths of the trapezium.
So in our case we'll do 4 plus 6 all over 2, and then times that by the height of 5. And if we simplify that, the 4 plus 6 is 10, and then the 10 divided by 2 is just 5. So we have 5 times 5. which is 25cm2. Then to finish we just add together the areas of the rectangle and the trapezium, so 180 plus 25, to get a total area of 205cm2. Anyway, that's everything for this video, so hope it was helpful. If you haven't seen it already, we now have a live past paper website up, so you can just click this button in the top right corner of this screen. and you can check out our new website.
Hope you enjoy!