Monday, March 31, 2008
Find out a way to get the area of triangle.
Let's look at rectangle. Imagine a triangle somewhere inside, but with two vertexes in the bottom two corners of the rectangle.
How can we find the area of the triangle? It must be smaller than the are of a rectangle since it fit's inside. The area of the rectangle is just the base time the height (b x h).
If we drop a line down what do we see?
We've split the triangle into two triangles, does that help us?
Actually, we've split it into four triangles, what can you see about these triangles?
Look at the two triangles at the right they look like they are the same size.
Yes they are the same size. Look all the lines are the same length.
So what have we learned?
We can split our original triangle into four triangles two of which are identical.
If we add up all the triangles together, what is it's area? It must be the area of the rectangle which we know is b x h.
So if the 4 triangles = b x h. What must be the size of the two triangles we care about?
It must be 1/2 b x h.
How can we find the area of the triangle? It must be smaller than the are of a rectangle since it fit's inside. The area of the rectangle is just the base time the height (b x h).
If we drop a line down what do we see?
We've split the triangle into two triangles, does that help us?
Actually, we've split it into four triangles, what can you see about these triangles?
Look at the two triangles at the right they look like they are the same size.
Yes they are the same size. Look all the lines are the same length.
So what have we learned?
We can split our original triangle into four triangles two of which are identical.
If we add up all the triangles together, what is it's area? It must be the area of the rectangle which we know is b x h.
So if the 4 triangles = b x h. What must be the size of the two triangles we care about?
It must be 1/2 b x h.
Labels: math
