Wednesday, 25 March 2009

Areas of triangles

I have looked at the area of simple shapes. I will now consider shapes that are a little more complex than squares and rectangles. Let's take a triangle. Have it in your mind that one side is horizontal, and the other two sides go upwards and inwards. From where these lines meet, take a vertical line down to the horizontal line and this is the height (h) of the triangle. The length of the horizontal line is the base (b).

How do we work out the area? This is where origami comes in. This works in a more complicated way for every triangle, but it is easier to explain if we pick on an isosceles triangle, that is the two angles from the base are the same. Fold that triangle in half from one end of the base to the other. You know the area is twice this size because you folded it in half. Another thing that is twice this size is the shape that makes the folded triangle into a rectangle. To make this rectangle you have to be able to unfold the triangle but this time along the long side (the hypotenuse).

Now you know that the area of a triangle is like the area of a rectangle that has the same height but only half the length. As usual, written explanation takes paragraphs. The mathematical thing to remember is that the area of a triangle is bh/2. Once you have the idea in your head it works for all triangles - it works every time.

That sums it up

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