Hi. I'm Peter Edwards from Bluetutors. We teach children of all ages right from primary school to degree level. We find the highest quality tutors. And today, I'm going to teach you some maths. So, now we're going to look at how to calculate the area of a triangle. So I'll tell you to start with work out the area, it's half of the base times the height of the triangle. But we should look at why that is. So, if you look at this example here, we have a triangle, we have its height and we have its base. The reason it's half base times the height is because if you imagine completing this quadrilateral, you can see that essentially we have two triangles there, one here and one here. And to work the area of that quadrilateral, it would be h times b, so to work out the area of the triangle, it's simply half of that. So if we look at a few examples, this first one here, we have the base being 3 and the height being 4. So to work out the area, it's one half times three times four which is six. If we say it's in centimetres, then we should put centimeters square next to it. So if we look at our next example, we have the base which is 4 and you'll notice that the perpendicular height is 10. We need to take the perpendicular height rather than the length of these two lines. So to work out the area, we have one half times four times ten which gives us twenty centimeters square. Okay. So let's look at the last example, here we haven't got the height so we actually have to work out the height before we start. Those of you who know Pythagoras, will know that this triangle is at three, four, five triangle. So I'll put four in there. If you want to check that you can see that twenty-five square is equal to, sorry, five square is equal to four square plus three square, twenty-five is equal to sixteen plus nine. So to work out the area of this triangle, it should be one half times three times four which again gives us six centimeters square. And that's how to work out the area of a triangle. .

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