Sherpa

2-dimensional shapes are flat. The perimeter of a 2D shape is the total distance around the outside of the shape. The area of a 2D shape is the space inside the shape. 2D shapes only have 2 dimensions, length and width. A polygon is known as a closed 2D shape with straight sides. Examples of polygons include triangles, quadrilaterals, pentagons, hexagons and octagons. Regular polygons have sides that are equal in length and have equal angles.

Today we're going to be looking at some 2D shapes, twodimensional shapes, some of the oldest things ever studied in mathematics, all the way back to the ancient Greeks, the Babylonians. Whether you're tiling the floor of a temple or you're trying to figure out how much grass to put on your lawn, you need to have the shape of whatever you're doing so that you can figure out how to fill it out. So the regular shapes here have all the same size, the same, which is why they have this symmetrical pattern. An irregular shape doesn't have the same size, the same. You might have some sides the same, but they're not all the same.

You need to know all of these names off by heart. But if we're looking at this irregular shape, what would you call this one? An irregular watt. So you count the number of sides up 123-4566 sides as a hexagon. Here's your regular hexagon.

So this shape here is an irregular hexagon. So now we're going to move on and just look into the areas and perimeters of some of some simple shapes.

Okay, up here we have a rectangle and it measures a length of ten and a width of four. And the area for a rectangle is LW times width. So here the area of this rectangle is simply ten centimetres times four centimetres, which is 40 centimetres squared. You measure area in centimetres square, metres square for the perimeter of the shape. That perimeter is the length of the outside edge.

You have to add up all the edges and make sure you don't forget these two missing ones here. There's a ten there and there's a four there. So the perimeter is all sides added together, which in this case is 28 centimetres. Again, lengths like perimeters are measured in centimetres. Areas such as the number of centimetres squares inside a shape are measured in centimetres squared.

And a compound shape here is made up in this example of two rectangles that can be made up of lots of things, triangles, circles. But for a compound shape, it's all the areas inside added together. So you break the shape down into two shapes that you recognise. So we're going to break this one horizontally. We could have done it vertically down there.

So we've got two rectangles and we know how to calculate the area of a rectangle. So we've got this shape two times. And a big mistake here is people might say two times eight. No, this is not eight. This whole length up and down is eight, but this one is three, which tells us that this missing length here is eight, subtract three five.

So we've got a two x five. So this is ten centimetres squared. This one here is our ten x three, which is 30 centimetre squared. And so the area of the compound shape is area 110 plus area 230. So we have 40 centimetre square.

And if you were going to do the perimeter. Just add up all the outside edges and make sure not to miss any of them. This one here we didn't write down, but this would be ten, subtract two, which would be eight. And then you would write down all the measurements.

Okay, parallelogram is next. The area of a parallelogram is essentially the same as the area of a rectangle. It's the length times the width. But we tend to say the base, the bottom of it times the height. It is not the diagonal slant, it's the vertical up and down height.

Would you measure your height horizontally or would you measure it at a diagonal slope? Of course, you'd measure it vertically, rather up and down. So that's how we measure the height, straight, vertically, up and down. So in this case, it's the base, which is ten. If it's ten along there, it's also ten down here, times the height five.

So we've just got ten times five or 50 centimer squared. So parallelograms, no reason to panic. Nice and straightforward. Area of a parallelogram is just the base times the height area of a triangle. Just to show you the error, triangle will cut this bit off.

We'll cut this bit off. Start writing with a pen. Brilliant. We'll cut this bit off up here and we'll just be left with this triangle at the bottom. And you'll see that a triangle is half of any parallelogram.

So the air of a triangle is a half of the area of the parallelogram. It's a half the base times the vertical height. So the area of any triangle is just half of the area of the parallelogram. So we've got half times ten times 525 centimetres squared.

And finally, the trapezium formula for the area of the trapezium is a half A plus B times the height. H, technically, is usually in half A plus BH. That's usually the same thing. It doesn't matter the order of multiplication. So essentially what it's saying is you take the top and the bottom and you add them together.

This is normally our A, the top, this normally our B. And H, of course, is the height. I've given them some numbers here. So it's the top plus the bottom A plus B times by the height, and then divided by two. So in this case, it's a half top plus bottom A plus B, which is three plus eleven times by the height, which is ten.

So we've got a half of 14 times ten, half of 140, and so we have 70 centimetres square. So that's how you do the area of a trapezium. It's a half A plus B times H, a half top plus bottom times the height.

Okay, just answer a couple of quick questions. This trapezium, it tells you what the area is, and we're asked to figure out this missing length X. So how do you calculate the area of this trapezium? That's right, how do you restart this one. Okay, now on to some quick questions.

This one, you are given the area of the strapesium, and you're asked to calculate this missing height, x. Well, how do you do that? Well, you start with your formula for the area, which you know is a half A plus B, top plus bottom times H. And you know, in this case, that's 63, because it tells you what the area is. So we have a half top is six, bottom is twelve times the height.

We don't know that. So that's x times the height, x is 63. So using your algebra, if you just rearrange this equation, six plus twelve is 18, half of that is nine. So we see that nine x is equal to 63, and so x is equal to 63 divided by nine x is equal to seven centimetres. So that's how these are done.

So, one for you to try a bit more of a complicated exam type question. Here, you are being asked to calculate H in this parallelogram, and you are told that the area of this parallelogram is three times the area of this triangle. You'll need to use your formulas for areas of triangles and parallelograms to figure out the answer h. If you wish to put your answers in the comments, feel free to do so.

If you give it a shot and you think you've got the right answer, please feel free to contact myself, my name is Adam tutor at Sherpa, or any other Sherpa tutor, and I'm sure that they can give you the answer in a jiffy. Thanks, guys. See you later. Bye.