Measurement 2.pdf

342 PEARSON mathematics 7 Paddocks Equipment required: 1 brain, graph paper The Big Question A farmer is planning to fence off an area of 400 m2 for the calves on his property. What dimensions (length and width) would give the paddock an area that is cheapest to fence? Engage 1 Shapes with the same area can have different perimeters. Each of the rectangles below has been made using 12 squares. Each square has a side length of 1 m. (a) Copy and complete the table below for the three rectangles. (b) Which of the rectangles above has the shortest perimeter? (c) Why would the farmer be interested in having the shortest perimeter? Explore 2 List all possible pairs of whole number dimensions that would give a paddock with an area of exactly 400 m2. 3 (a) Select three of the paddocks you think are most suitable for containing the calves. Draw the three paddocks on graph paper, showing their dimensions. To show their relative sizes, use a scale of 1 cm on page = 5 m in real life. (b) Find the perimeter of each of the three paddocks. 4 Use the following information to complete the table on the following page and calculate the total cost of the fencing for each paddock. Fencing wire: Each fence has five strands of wire. Each strand goes all the way around the fence. The wire costs 85c per metre. Corner posts: The paddocks will need a large post at each corner, each costing $40. Standard posts: There must be a post at least every 5 m along a section of fence. If the distance between the corner posts is longer than 5 m, a standard post is placed along the fence. Mark where the standard posts will be required on the diagrams of each of your paddocks, and count the number needed for each paddock. Each standard post costs $15. 1 m Dimensions of shape Area (m2) Perimeter (m) 1 × 12 2 × 6 3 × 4 ? Draw a diagram. ? Test all possible combinations. Strategy options Investigation AA Pearson Maths 7 SB-06.fm Page 342 Wednesday, August 10, 2011 9:33 AM 6