Wendy C. answered • 04/21/15
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To add onto the above answer.
In order to understand dilation, you have to understand that when a triangle, or any other shape, is dilated, its sides shrink by the dilation ratio.
The perimeter of triangle is X + Y + Z, where X, Y, and Z are the sides. So if we shrink all the sides by 2/5, we change the perimeter by 2/5.
However, because the area of the triangle involves 0.5 Base * Height, if we shrink all of the sides by 2/5, the area is shrunk by 2/5 * 2/5 (once for base, once for height).
The above applies for squares and other polygons as well. 3-D objects like cylinders and spheres are more complicated still.
Good luck on your other questions!
