Darren is building a rectangular frame for a children's sandbox with 40 cm of lumber.
a) Let each toothpick represent 1 m of lumber. Construct different rectangles to represent the sandbox's area. Recor the dimensions and the area in each case.
b) How many different rectangles are possible?
c) Which shape would you choose for the sandbox? Give reasons for your choice.
A rectangular flow garden is to have an area of
16 m^2. Edging bricks will be used to form the perimeter of the garden.
a) On grid paper, sketch all the rectangles with whole-number dimensions and an area of 16
b) Which shape would be the most economical for the garden?
A whiteboard is to have an area of
1 m^2. What should the dimensions of the whiteboard be to minimize the amount of framing required to go around the outside?
What is the maximum area of a rectangular yard that can be enclosed with 120 m of fencing in each case?
a) The yard is enclosed on all four sides.
b) The yard is enclosed on three sides.
A rectangular skating rink is to have an area of
m^2. The rink is surrounded by boards.
a) What are the dimensions of the rink that can be enclosed most economically?
b) Give reasons why the rink might not be designed in the most economical shape that you determined in part a).
A 3L box of rice is square-based prism and is to be made from the minimum amount of cardboard. Determine the minimum amount of cardboard required, to the nearest square centimeter.