Triangle Area
- Author:
- user2052
- Topic:
- Area
Points A, B, and C are moveable, feel free to drag it around.
First, note the yellow dashed lines, they are drawn to the midpoints of the blue, red, and green segments (half of each create the small interior triangle, area of which is 3)
Focus on the blue segment triangles (triangle A'BC and triangle A'B'C). Note that they both have congruent bases (blue segments BC and B'C) and the same height A'G, thus these two triangles are congruent.
Next, let's look at triangle A'BC and triangle ABC (remember, we know the area of this is 3!). Note, they have congruent bases AB and A'B (the red segments) and the same height CH, so they have equal areas of 3.
This means A'B'C has area 3 (since we proved it is congruent to A'BC).
Similarly, you can show the rest of the triangles have equal area to ABC, and thus there are 7 small triangles of area 3 that comprise the large triangle A'B'C', so the A'B'C' has area 21.