Area & Perimeter

G 1 2
Ask students to calculate the areas of each rectangle.
Examples involving decimals can be done on a calculator.
You may want to suggest rewriting a length involving
fractions; for example, 6 1 ⁄4 = 6.25.
Distribute copies of Worksheet G12(a).
T: This farmer also wants to build pens that have
the largest possible area. Investigate the problem
and record solutions on your worksheets.
If many students believe the largest area is 624 m 2 for rectangles of dimensions 12 m by 52 m and
13 m by 48 m, suggest trying a width between 12 m and 13 m. Students may notice that when they
increase blue segments by 1 m they must correspondingly decrease the red segment by 4 m. Also,
students should begin observing in these farmer problems that you can increase the blue segments
only so much before you begin decreasing area.
When the class concludes that a pen 12.5 m by 50 m
is the best size for the farmer, pose a similar
problem with four pens. Distribute copies of
Worksheet G12(b) for students to record solutions.
The class should find that the best solution in this
case is a pen 10 m by 50 m.
Illustrate these four situations on the board.
T: What patterns do you notice (point to the illustration of the pen with one section, with three
sections, and with four sections)?
S: The red length is always 50 m.
T: So the farmer uses half of the fencing for the length of the pen and must use the other half
to make the sections. If a farmer only wanted two sections (point to the appropriate
illustration), what might you expect the length of the pen to be?
S: 50 m.
G-62
IG-III