Geometry 9-5 Changing Dimensions (Proportionally)

If you change each dimension of a figure, the figure will be similar only larger or smaller.

Double each dimension

Divide each dimension by 33 in

8 in

6 in

16 in

5 in

12 in

4 in15 in

Area and PerimeterWhat is the effect on area and perimeter?

Ex) triple each dimension of rectangle

2 in

5 in

6 in

15 in

𝐴=2∙5=10𝑃=2+2+5+5=14 𝐴=6 ∙15=90

𝑃=6+6+15+15=42𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=

𝑃𝑁𝑒𝑤

𝑃𝑂𝑙𝑑

=4214

=3𝐴𝑟𝑒𝑎=𝐴𝑁𝑒𝑤

𝐴𝑂𝑙𝑑

=9010

=9

Shortcut?The effect on the area can be found by multiplying the changes in each dimension.

The effect on the perimeter is the same as the change for each dimension (only if each dimension is changed by the same factor)

Example

If both diagonals of a rhombus are doubled, what is the effect on the area and perimeter?

If each dimension of a triangle is divided by 3, what is the effect on the area and perimeter?

Area: 2 x 2 = multiplied by 4

Area: x = multiplied by

Perimeter: multiplied by 2

Perimeter: multiplied by

Example

The dimensions of a triangle are changed proportionally such that its area changes by a factor of . How were the dimensions changed?

Area: x = , so the dimensions were multiplied by

Special Case: Circles

The formula for circles only uses one variable, r.However, the radius represents both the “base” and the “height” of a circle.

r

r

Ex) If the radius of a circle is doubled, then the…

area is _________perimeter is ________

quadrupled

doubled