Transcript Geometry 9-5 Changing Dimensions (Non

Geometry 9-5 Changing Dimensions
(Proportionally)
If you change each dimension of a figure, the
figure will be similar only larger or smaller.
8 in
Divide each
dimension by 3
3 in
5 in
15 in
Double each
dimension
4 in
16 in
6 in
12 in
Area and Perimeter
What is the effect on area and perimeter?
Ex) triple each dimension of rectangle
15 in
5 in
2 in
6 in
𝐴 = 2 ∙ 5 = 10
𝑃 = 2 + 2 + 5 + 5 = 14
𝑃𝑁𝑒𝑤 42
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 =
=
=3
𝑃𝑂𝑙𝑑
14
𝐴 = 6 ∙ 15 = 90
𝑃 = 6 + 6 + 15 + 15 = 42
𝐴𝑁𝑒𝑤 90
𝐴𝑟𝑒𝑎 =
=
=9
𝐴𝑂𝑙𝑑
10
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?
Area: 2 x 2 = multiplied by 4
Perimeter: multiplied by 2
If each dimension of a triangle is divided by 3,
what is the effect on the area and perimeter?
1
3
1
3
Area: x = multiplied by
Perimeter: multiplied by
1
3
1
9
Example
The dimensions of a triangle are changed
proportionally such that its area changes by a
1
factor of . How were the dimensions changed?
16
1
4
1
4
Area: x =
1
,
16
so the dimensions were multiplied by
1
4
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…
quadrupled
area is _________
doubled
perimeter is ________