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What is the total area of the house and garage and the cost to maintain the lawn?

Mathematics

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Here are the solutions to the questions:

  1. The total area of the house and garage is...
  1. Calculate the area of the house.

    $$
    \text{Area of House} = \text{length} \times \text{width} = 15 \text{ m} \times 10 \text{ m} = 150 \text{ m}^2
    $$
    
  2. Calculate the area of the garage.

    $$
    \text{Area of Garage} = \text{length} \times \text{width} = 5 \text{ m} \times 4 \text{ m} = 20 \text{ m}^2
    $$
    
  3. Add the areas of the house and garage to find the total area.

    $$
    \text{Total Area} = 150 \text{ m}^2 + 20 \text{ m}^2 = 170 \text{ m}^2
    $$
    The total area of the house and garage is $\boxed{\text{170 m}^2}$.
    

    2. What will it cost per 6 month contract to get this company to look after the lawn?

  4. Calculate the total area of the property.

    $$
    \text{Total Property Area} = \text{length} \times \text{width} = 40 \text{ m} \times 20 \text{ m} = 800 \text{ m}^2
    $$
    
  5. Determine the area of the lawn.

    The unshaded area is the lawn. Area of Lawn=Total Property Area−(Area of House+Area of Garage) \text{Area of Lawn} = \text{Total Property Area} - (\text{Area of House} + \text{Area of Garage}) Using the result from Question 1: Area of Lawn=800 m2−170 m2=630 m2 \text{Area of Lawn} = 800 \text{ m}^2 - 170 \text{ m}^2 = 630 \text{ m}^2

  6. Calculate the cost for the 6-month contract.

    The charge is R2,50 per m2\text{m}^2. Cost=Area of Lawn×Rate per m2 \text{Cost} = \text{Area of Lawn} \times \text{Rate per m}^2 Cost=630 m2×R2.50/m2=R1575.00 \text{Cost} = 630 \text{ m}^2 \times R2.50/\text{m}^2 = R1575.00 The cost for the 6-month contract is R1 575,00\boxed{\text{R1 575,00}}.

    1. The perimeter of this property is...
  7. Identify the dimensions of the entire property.

    The property is a rectangle with a length of $40 \text{ m}$ and a width of $20 \text{ m}$.
    
  8. Use the formula for the perimeter of a rectangle.

    $$
    \text{Perimeter} = 2 \times (\text{length} + \text{width})
    $$
    $$
    \text{Perimeter} = 2 \times (40 \text{ m} + 20 \text{ m})
    $$
    
  9. Calculate the perimeter.

    $$
    \text{Perimeter} = 2 \times (60 \text{ m}) = 120 \text{ m}
    $$
    The perimeter of this property is $\boxed{\text{120 m}}$.
    
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