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Peters Gardening Service By Emma Klapste 8K Slide 2 Peter is a professional gardener who tends the gardens and lawns of his many clients. One of his jobs is to fertiliser the lawns regularly. He is trying a new fertiliser which, according to the directions, states that when the contents of the container are mixed with water solution covers 64m2 of lawn. To help him decided how many containers of fertiliser he may require, Peter needs to have some idea of possible sizes of lawn one container will cover. Equations Investigation Slide 3 Peter needs to find length of the square with area of 64m2. the length of the square is represented by X. The equation for a square lawn would be area = X2 First Peter considers a square lawn. L x L = 64m2 = 64m = 8 X = 8 8 8 8 8 Slide 4 Most of Peters clients dont have square lawns. Peter needs to figure out what lawns are covered by one container of fertiliser. To work out the area of a rectangle is Length X Width =Area which is 64m2. If the width was 1m the length would be 64m, 1 X 64 = 64m2. If the width was 2m the length would be 32m, 2 X 32 = 64m2. If the width was 4m the length would be 16m, 4 X 16 = 64m2. If the width was 5m the length would be 12.8m, 5 X 12.8 = 64m2. If the width was 10m the length would be 6.4m, 10 X 6.4 = 64m2. Next Peter consider a Rectangle lawn. L W Slide 5 Triangular lawns can come in many shapes and sizes so Peter needs to work out a range of areas for different triangular lawns. To work out the area of a triangle you must times X b X h = Area. If the base was 8m then the height would be 16m, X 8 X 16 = 64m2. If the base was 13m then the height would be 9.85m, X 13 X 9.85 = 64m2. If the base was 3m then the height would be 42.66 m, X 3 X 42.66 = 64m2. If the base was 4m then the height was 32m, X 4 X 32 = 64m2. If the base was 7m then the height would be 18.28m, X 7 X 18.28 = 64m2. To work out the height of a triangle is 64 b 0.5 = h. Then Peter Considers a Triangular Lawn H B Slide 6 Peter thought of how some of his clients may have circular lawns but they may be different sizes. To figure out the area of a circle is area = R2. Only one circle has the area of 64m2, the radius is 4.52, the equation to getting this answer is 64 (3.124) = 20.486556. 20.486556 = 4.52 (R). Next Peter Considered a Circular Lawn. R Slide 7 Peter thought about how there are lawns that are much different to others so he considered a L-shape lawn. An L- shape lawn is just three squares or one rectangle and a square to form the shape of an L. To figure out the area of this shape you use the formula A = L2 X 3. The equation I used was 64 3 = 21.33 then 21.33 = 4.6 (L). 4.6 X 4.6 = 64m2. Then Lastly Peter Considered A L- Shaped Lawn. L L L L Slide 8 I choose a Trapezium. To work out the area of a Trapezium is Area = (a+b) h. If A was 10m and base was 6m then height would be 96m, (10 + 6) X 96 = 64m2. If A was 2m and base was 15m then height would be 58m, ( 20 + 15) X 58 = 64m2. If A was 17m and base was 11m then height would be 72m, (17+ 11) X 72 = 64m2. To work out the height of the Trapezium you do the equation 64 (a + b) = h. My Own Shape. A B H Slide 9 BY EMMA KLAPSTE 8K