Imperial Area: Working With Square Units Again: Activity: 1) Cut out two squares that each have a side length of one foot. 2) What is the area of each square in square feet? 3) Take one of those squares you just made, and divide it into little squares that have a side length of 1 inch. You don't need to cut them out, however, use a marker to show all of the little squares. 4) How many little squares are equal to the larger square? So What is the area of the original square in square inches? 5) As a class, we will make a square with side lengths of 1 yard. 6) what is the area of this new square in... square yards? square feet? and square inches? 1
Summary: Example: Dawn bought wallpaper for her bedroom. The roll of wallpaper is in wide. Dawn s walls are 8 ft high. She plans to cover the walls in vertical strips from floor to ceiling. What is the area that can be covered with one vertical strip of wallpaper? 2
Big Areas: In the imperial system the acre and square mile are used to describe areas too large to be easily described by the square foot or square yard. The acre was originally defined as the area of a field that could be ploughed by a single ox in one day. The word acre comes from the Old English word aecer, meaning field. In the nineteenth century, surveyors mapped Western Canada. The land was divided into squares that measured 6 mi on a side. These large squares were called townships. A square mile was called a section, so there were 36 sections in a township. Each section was divided into quarters, orquarter sections. Each quarter section was one half mile. These quarter sections were parcelled out as homesteads. Each quarter section was 160 ac in size. An acre, an imperial area measurement, is a square that measures approximately 70 yd on a side. 3
Example: An American football field is 360 ft 160 ft. Is its area much smaller than, roughly the same as, or much larger than 1 ac? Converting Imperial and SI units of Area Example: Convert 1 in 2 to square centimetres. 4
Similar to how we did the previous example, complete the following charts: Example: The area of Jasper s living room is 180 ft 2. What is the area in square metres? 5
Practice: SC 1. Jasper wants to install a parquet floor in his kitchen. He sees an advertisement in a flyer that quotes prices per square foot. About how many square feet will Jasper need if the floor is a rectangle measuring 10 ft 9 in 11 ft 6 in? SC 2. A sheet of printer paper is 8.5 in 11 in. Darcy says it is almost 1 ft 2. Is Darcy correct? Explain your answer. SC 3. Paula purchased a new home 1260 ft 2 in area. What is the home s area in square yards? SC 4. Boris s front lawn is rectangular and measures 50 ft 30 ft. He purchased a fall fertilizer that must be applied at a rate of 6 lb per 1000 ft 2. How many pounds of fertilizer should Boris apply? SC 5. The sole of each of Norma s moccasins is 36 in 2 in area. When Norma stands with both feet flat on the floor, what is the total area in square feet that the moccasins cover? 6
SC 7. There are 160 ac in a quarter section. How many acres are there in a section that is 1 mi 2 in area? SC 8. When the Doukhobors immigrated to Canada from Russia in 1899, they were granted 773 400 ac for their farms and communities in what is now Saskatchewan and Manitoba. What is the area of this land grant in square miles? SC 9. According to the United States Department of Agriculture, in 2009, American farmers planted 320.9 million acres to principal crops. What is this acreage in square miles? SC 10. Using your answer from question 9, how long would the sides of a square be that enclosed 320.9 million acres? Express your answer to the nearest mile. How do you find the side length of any square from its area? For example, what is the side length of a square having an area of 9 mi2? 7
SC 13. Nick planted 320 ac of canola. How many hectares of canola did he plant? Round your answer to 1 decimal place. SC 14. The area of Morris s front lawn is 100 yd 2. What is the area in square metres? Round your answer to the nearest unit. SC 15. The printed area of a wedding invitation is 150 cm 2. What is the area in square inches? Round your answer to 1 decimal place. 8
9
10