GANSBAAI ACADEMIA

MATHEMATICS
Grade 12 / /

INVESTIGATION

March 2014

Total: 70
Time: 2 weeks
EXAMINATOR
MODERATOR / L. Havenga
L. Mostert

THE PROBLEM: To investigate the polygon that has the largest area with a fixed perimeter

MEMO

TASK 1

1. How many different triangles can you make with a perimeter of 12 units?

2. Use integer values for the lengths of the sides or use 12 matchsticks to investigate how to
make up your triangles.

3. Find the area of each triangle and decide which has the greatest area.

TASK 2

1. How many different rectangles can you make with a perimeter of 12 units?

2. Use integer values for the lengths of the sides or use 12 matchsticks to investigate how to
make up your rectangles.

3. Find the area of each rectangles and decide which has the greatest area.

TASK 3

1. Use your results from Task 1 and 2 to make a conjecture about the type of polygon that,
with the same number of sides, will give a maximum area.

TASK 4

1. Investigate the areas of regular polygons with a fixed perimeter of 12 units..

2. Calculate the length of the side of each polygon. This does not have to be an integer value; use
this information to find the area..

(HINT: divide the polygons into triangles and use these to find the area of each polygon.)

3. Investigate polygons with 3, 4, 6, 8 and 12 sides.

4. Lastly, calculate the area of a circle with a perimeter or circumference of 12 units.

TASK 5

1. If you knew that two regular polygons had the same perimeter, describe in words how you would
predict which one had the greater area.

2. Use in your results from Task 4 to make a conjecture about the type of polygon or figure that
yields a maximum area, given a fixed perimeter.

1

RUBRIC

NAME AND SURNAME: GR 12A

MARKS / 0-3 / 4-7 / 8-10 / Tot
Choice and length of sides / Most lengths of sides are incorrect / At least half of the choices and lengths of sides are correct. / All choices and lengths of sides are correct. / 10
Diagrams / Many diagrams incorrect and do not accurately represent the polygons. / At least half of the diagrams are correct, but poorly drawn, and construction lines are not shown. / Diagrams are neat and accurate.
All construction lines are shown. / 10
Area calculations / Inaccurate calculation OR answers only and no steps are shown. / Most calculations are correct, but not all working out is shown. / All calculations are accurate and all steps are shown. / (10X3)
30
Conclusions and Conjectures / Some conclusions are correct but no conjectures are correct. / All conclusions correct, but conjectures are not worded appropriately. / All correct.
Conjectures are well communicated and accurate. / 10
Neatness and presentation / Layout, logic and presentation are poor. / Satisfactory layout and presentation, but arguments are average. / General presentation and layout are excellent. / 10
70

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