Grade 8 Math Discovery Chapter 10 Section 1
NAME: ______
OUTCOMES COVERED:
D2 solve measurement problems, using appropriate SI units
D5 describe patterns and generalize the relationships between areas and perimeters of quadrilaterals
Part B: What is the minimum perimeter required to surround a given rectangular area?
You are designing a rectangular playground for young children. The playground must have an area of
24 m2. What is the minimum total length of fencing needed to completely enclose the playground?
BE SURE TO INCLUDE UNITS IN ALL MEASUREMENTS AND CALCULATIONS!!
1. a) Build a rectangle using the 24 square tiles given (CALL THIS RECTANGLE A). Make sure you use all the tiles and that you have no gaps in the rectangle.
b) Complete the table below with your results from above.
Rectangle / Length (m) / Width (m) / Perimeter (m) / Area (m2)A
B
C
D
2. If you make a different rectangle that has the same area, do you think it will have the same perimeter? Explain your thinking.
3. a) Use the tiles build a different rectangle that has an area of 24 m2.
b) Compare your new rectangle to the first rectangle. Do you think the perimeter of the new rectangle will be greater than, less than, or equal to the perimeter of the first rectangle.
c) Fill in the table for the new rectangle (CALL THIS RECTANGLE B). Was your prediction correct?
Explain.
4. a) Use the tiles or cubes to find as many rectangles as you can that have an area of 24 m2 (CALL THESE RECTANGLES C AND D).
b) Predict which rectangle has the smallest perimeter. Explain your thinking.
c) Measure the length, width, and perimeter of each rectangle and fill it in your chart. Was your prediction in above correct?
5. Suppose that you could use fractions or decimals for the length and width of the playground. If the area of the playground is 40 m2, what is the smallest perimeter possible? Round your answer to one decimal
place. Explain your findings using words and diagrams.
6. Reflection
a) Do all rectangles with the same area have the same perimeter? Provide an example to support your answer.
b) What type of rectangle will give a minimum perimeter for a given area?