Similarity

Similarity – Darshil Shah Similarity is the relationship between two- or three-dimensional figures having the same shape but not necessarily the same size. The angle of two similar polygons or solids is equal, but the lengths of the sides are only proportional.

If one side of a figure, Q, is twice the length of the corresponding side of a similar figure, R, then all of figure Q’s sides will be twice the length of the corresponding sides of figure R. A double-size enlargement of a photograph, for example, is similar to the original. In the enlargement all the distances in the original picture are increased by a factor of two. We can relate and calculate the various measurements of similar shapes by using a Scale Factor Scale Factor = length of new figure / length of new figure

Area of Similar Shapes When finding the area, the sides must be in proportion and therefore here must be a ratio. The total area is the amount of ratio on both sides. If the ratio is 1:2 then the area would be 1u2 and 4u2 (if the sides are 1 and 2 u long) Example

Volume of Similar Shapes When finding volume the sides again have to be in proportion to each other. When you find the area there are only 2 dimensions, but in volume you have to add another one. Therefore, if the ratio is 1:3, the total volume will be 1u 3 and 9u3 (if the sides are 1 and 3 u). If the height is in proportion to one another, then the area’s ratio will also be.