Relationship Between Scale Factor and Area
- Author:
- PDST PP Maths Team
1. Click the tick boxes in the first column first, then the second column, and finally the last column.
2. ''Side Lengths'' shows the side lengths of the two triangles; to show the two triangles are similar.
3. ''Next Step'' shows the perpendicular height of both triangles.
The second triangle has a perpendiular height that is k times the perpendicular height of the triangle on the left.
4. ''Area of Object'' will show the area of the triangle on the left.
5. ''Area of Image'' will show the area of the triangle on the right.
6. All distances in the image will be k times distances in the object, but is the area of the image k times the area of the object?
No, unless k equals 1.
7. If the relationship between the areas isn't k, then what is it? Let's have a look at other examples.
8. Adjust the slider k to 3.
With this second example it might now be possible to see that the area of the image is k² times the area of the object.
9. Adjust the slider k to 2.
10. ''Less specific and more general'' shows the areas of both triangles,
with the bases and heights in terms of x and h and the value of k is used.
11. ''General' shows the areas of the both triangles terms of x, h, and k.
This shows that, general, the area of the image is k² times the area of the object.
12. ''Move point C'' lets you drag one of the vertices in the object.
13. ''Vertices'' lets you drag points A, B and, C.
14. ''Lines'' shows the location of the centre of enlargement.