Garden Materials Help: Calculate Circumference, Perimeter, Areas & Costs

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SUMMARY

This discussion focuses on calculating the dimensions and costs associated with landscaping a garden, specifically for a pond, patio, and lawn. Key calculations include the circumference of the pond at 8.48m, the perimeter of the garden at 24.58m, and the areas of the patio (3.72m²) and lawn (13.5m²). The total cost for materials, including fencing, trellis, border blocks, patio slabs, and lawn food, amounts to £299. Feedback highlights the need for clearer trigonometric calculations and consistency in area measurements.

PREREQUISITES
  • Basic geometry concepts for calculating circumference and area
  • Understanding of trigonometry for perimeter calculations
  • Knowledge of unit conversions (cm to m)
  • Familiarity with cost estimation for landscaping materials
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  • Research methods for calculating the area of irregular shapes in landscaping
  • Learn about trigonometric functions and their applications in real-world measurements
  • Explore material cost estimation techniques for landscaping projects
  • Study best practices for documenting calculations in project assessments
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Homeowners planning garden landscaping, landscape architects, and students studying geometry and trigonometry in practical applications.

lward100
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Hi help please
You have decided to landscape your back garden, and have chosen to:

place a border around your pond (A)
replace the broken fence surrounding the garden and add a decorative trellis
build a patio in section B
spray your lawn with lawn food (it's looking a little patchy)
You can find a outline of your garden in Unit 2 - Assessment Resource.

You may find it helpful to print it out to view as you work through this assessment.

Part 1
Before you buy materials, you need to work out how much you will need. As such, you need to calculate the following:

the circumference of the pond
the perimeter of the garden
the patio area
the lawn area
the pond area
Please remember to show your workings and give answers to two decimal places!

Part 2
You have arrived at the store and managed to find everything you need. You now need to work out how much each of the materials will cost:

Fencing is £6 per panel
Trellis panelling is £8 per panel
Fencing and trellis panels are 1.5m in length
Border blocks for water features cost £5.40 per bag. Each bag covers 2m
Patio slabs are £9.50 per box of 10. Each patio slab measures 60cm x 60cm
Lawn food costs £3 per bottle. Each bottle covers 3 square metres
Remember to show your workings, and to provide a total cost at the end.

I submitted this - Circumference of the pond = pi*D = 2.7*pi = 8.48m
Perimeter of the garden = 6.2+7.4+(2.5÷tan(40))+2.5+5.5
Area of patio = 0.5(2.5)(2.5÷tan(40))
Perimeter of Garden = 6.2+7.4+(2.5÷tan(40))+2.5+5.5 = 24.58m
Area of patio = 0.5(2.5)(2.5÷tan(40)) = 3.72m^2
Area of lawn = area of garden - area of patio - area of pond = 0.5(5.5+2.5+7.4)(2.5÷tan(40)) - 0.5(2.5)(2.5÷tan(40)) - pi(2.7÷2)^2 = 13.5m^2
Area of pond = pi(2.7÷2)^2 = 5.73m^2

The circumference of the pond is 8.48m and each border takes 2m so 8.48÷2 = 4.24 = 5 border bags required therefore cost of border on pond = 5*5.40 = £27

The perimeter of the garden is 24.58m and each panel takes 1.5m so 24.58÷1.5 = 16.37 = 17 panels required.
The number of panels for fencing and decorative trellis is same so cost for both fencing and trellis = (17*6)+(17*8) =£238
Are of patio is 4.08 and each slab covers and area of (0.6)^2 so 4.08÷(0.6)^2 = 11.33 = 12 slabs required and so the total cost will be 12*9.5 = £114
Area of patio 4.08m^2 and each slab covers (0.6)^2 of area so 4.08÷(0.6)^2 = 11.33 = 12 slabs required which means 2 boxes required and so cost = 2*9.5 = £19
Area of patio 3.72m^2 and each slab covers (0.6)^2 of area so 3.72÷(0.6)^2 = 11.33 = 10.34 slabs required which means 2 boxes required and so cost = 2*9.5 = £19
Area of lawn = 13.5 and each bottle of lawn food is covering 3m^2 of area so 13.5÷3 = 4.5 = 5 bottles of lawn food required and hence the cost is 5*3 =£15
Total cost £299

Got this feedback-
Part A

Edge of the side of the house
You still have not shown the steps to work out trigonometry, including rearranging the equation and then solving it, once you have this you can just put the measurement length of the side of the house rather than (2.5 divided by tan (40) each time.

Area of lawn
Just need to include your answer here once calculated
Part 2
Area of patio
You have two results here and both differ from your answer in part 1, you also need to show the conversion from cm to m for the patio slabs. You are told each one is 60cm by 60cm, what is this in m2?View attachment 8552
 

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