This lesson you’ll explore the effect on dimension changes in perimeter
of the regular
polygons and circles, when their one or more dimensions is changed. The presentation
covering such content will be done by the instructor in own handwriting, and with
the help of several examples with solution and you can watch video. This will help
you understand and apply the relationship for perimeter related problem solving.
It covers the ideas of math changing dimensions of geometry shapes E.g.
you may be asked to change the dimension in some way shape- say double or
triple the dimensions of a given figure and find the perimeter of the
resulting figure. For example, if the dimensions of a given rectangular
shape lawn are 6 feet by 4 feet, then doubling the dimensions would result
in a rectangle with dimensions of 12 feet by 8 feet. The perimeter of the
resulting figure would be doubled i.e. it would be 2(12+8) = 40 feet.
Look at another example, where the perimeter of a square will be doubled,
if its side is doubled.
(More text below video...)
Note: If two polygons are similar, the ratio of perimeters is equal to the ratio
of the measures of the corresponding sides.
For example; in Fig: 1, rectangles ADCB and A'D'C'B' are similar.
Thus, AD/A'D' = 3/2, DC/D'C' = 6/4=3/2, CB/C'B' = 3/2 and BA/B'A' =6/4 =3/2.
Perimeter of ADCB/Perimeter of A'D'C'B' = (3+6+3+6)/ (2+4+2+4) = 18/12 =3/2.
Notice that the lengths of corresponding sides, is 3/2 and the ratio of the perimeters is also 3/2.
Look at another example: If two triangles are similar, the ratio of perimeter is equal to
the ratio of measures of the corresponding sides. In Fig: 2 (Not to Scale),
The perimeter of ABC = (42+26+40) = 108 units
The perimeter of A’B’C’ = (21+13+20) = 54 units
Ratio: Perimeter of ABC/ perimeter of A'B'C' = 108/54 = 2/1
It may be thus seen that the ratio of the perimeters of these similar triangles is the same as the ratio of the measures of the corresponding sides.
This statement is true for similar polygons of more than three sides as seen above.
Remember: When the dimensions of a figure are changed proportionally, the figure will be similar to
the original figure. E.g. if the radius of a circle or the side length of a square is changed;
the size of the entire figure changes proportionally.
Effects of Changing Dimensions Proportionally
Change in Dimensions
Perimeter of Circumference
All Dimensions* (a)
Change by factor (a)
The video above will explains in more detail on solving problems related to
changing
geometric dimensions and its effects on perimeter, including
watch video lessons
and practice questions with solutions.
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