Predict and calculate how changing one or more dimensions of a shape affects the shape's area.

1. Obj. 57 Effects of Changing Dimensions
The student is able to (I can):
• Predict and calculate how changing one or more
dimensions of a shape affects the area of that shape.

2. What happens to the perimeter and area of
a figure when we change dimensions
proportionally?
Example: What is the new perimeter and
area of the rectangle if the height is
doubled?
6
3
7
7
P = 2(3)+2(7)
= 20
P = 2(6)+2(7)
= 26
A = (3)(7) = 21
A = (6)(7) = 42

3. Example
(cont.)
Now, what would be the effect if the
rectangle’s base were doubled?
3
3
7
P = 2(3)+2(7)
= 20
A = (3)(7) = 21
14
P = 2(3)+2(14)
= 34
A = (3)(14) = 42
Notice that in both cases, doubling one
dimension doubles the area. It doesn’t
matter whether it is the base or the height.

4. What happens if we double both the base
and the height?
P = 20; A = 21
3
7
6
14
P = 2(6)+2(14)
= 40
A = (6)(14)
= 84
This time, the perimeter doubled, but the
area changed by a factor of 4. Why the
difference?

5. Let’s break down the area on the last
example:
2(3)
2(7)
P = 2[2(3)]+2[2(7)] A = (2)(3)(2)(7)
= (2)(2)(3)(7)
= 2[2(3)+2(7)]
= (4)(21)
= 2(20)
= 84
= 40
Both sides are multiplied by 2, so the
perimeter is doubled and the area is
multiplied by 22.

6. Now, let’s look at a circle. What happens to
the circumference and area if we triple the
radius?
•
2
•
6
C = 2π(2)=4π
A=π(22) = 4π
The circumference
increased by 3, and
the area increased by
32 or 9.
C = 2π(6) = 12π
A = π(62) = 36π

7. We can use these ideas to work problems
going the other way:
1. If a square’s area is quadrupled (x4),
what happens to the perimeter?
Since the area is multiplied by 4, that
means that each side was multiplied by
the 4 or 2. Thus, the perimeter is
doubled.
2. If a circle’s circumference is reduced by
half, what happens to the area?
If the circumference is multiplied by ½,
then so is the radius. Therefore, the
2
1 ) or ¼.
area would be multiplied by ( 2