Hi, I'm Steve Jones and I'm going to tell you something about calculating the surface areas of basic 3D shapes. Now these are some very basic 3D shapes, you've got cube, a rectangular prism, a pyramid; but this is a very strange shape, I just illustrated with two different shapes which is a square and a pentangle and if you look at the modern football, you will find that the surface is actually covered by this. So you might try and estimate the area of those too. But what is very easy, first of all, such a shapes as a pyramid. The pyramid consist of, in this case, a four, a square pyramid, consists of five surfaces; one, two, at the back, three, on this side, four and the base five. Here we have four triangles and one rectangle. The triangles, we use the formula, 1/2 the base times the height, perpendicular height. And the rectangle, length times width. So then, we can work out the surface area by working out the individual areas, adding them together. A cube is very simple, because a cube is always the same dimension. So it has six sides, each is l times l, which is l squared. I can work out therefore this size the area of one side and then multiply it by six, I get the surface area. With the rectangular prism like this one, I have two ends, I have two sides and I have two other sides of a different size. So I dot it in six sections. This, on the one, at the back, I can't, see; this on the one on the left I can't see, the top and the bottom. Determining each of these, each of these as length times width and add them together. So here, I first of all count the surfaces. Secondly, I measure and calculate each area and then thirdly, I add the areas together. A football is an example where the, they are not the same, I need to count the number of pentangles. I need to count the number of squares. I need to calculate the areas of the squares, there, the pentangle; to calculate the area of a pentangle of course, I turn it into triangles so I can work out three triangles, right, add them together, the square and then from the numbers, multiplied by the areas, I can work out the surface area, of quite a complex shape, a football. So this is simple, the working of the surface areas of some of the more simple, basic 3D shapes.
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