Question

Imagine that you are in charge of planning a town park. The park will be shaped like a square. The community council has given you these guidelines: . At least \(12 \%\) of the park must be a picnic area. ?Between \(15 \%\) and \(30 \%\) of the park should be a play area with a sandbox and playground equipment A goldfish pond should occupy no more than \(10 \%\) of the park. On a 100 -grid, sketch a plan for your park. You may include any features you want as long as the park satisfies the council's guidelines. Label the features of your park, including the picnic area, play area, and goldfish pond, and tell what percent of the park each feature will occupy.

Short answer

Picnic area: at least 12%, play area: 15-30%, goldfish pond: no more than 10%.

Step-by-step solution

Determine the size of the park

The park is shaped like a square and can be scaled to a 100-grid, which suggests a 10x10 grid.

Calculate the minimum picnic area

At least 12% of the park must be a picnic area. On a 100-grid, this is \[ 0.12 \times 100 = 12 \text{ squares} \]

Determine the range for the play area

The play area must be between 15% and 30% of the park. Calculate the range: \[ 0.15 \times 100 = 15 \text{ squares} \] and \[ 0.30 \times 100 = 30 \text{ squares} \]

Calculate the maximum goldfish pond area

The goldfish pond can occupy no more than 10% of the park. Calculate this as: \[ 0.10 \times 100 = 10 \text{ squares} \]

Sketch the plan

Create a 10x10 grid for the park. Ensure that the picnic area is at least 12 squares, the play area is between 15 and 30 squares, and the goldfish pond is no more than 10 squares. Label each area with the calculated percentages.

Key concepts

Area Calculation

Area calculation is essential in many real-world applications, including planning a park. The exercise involves a square park laid out on a 100-square grid, representing a 10x10 grid. The total area of the park can be calculated using:
\[ \text{Total Area} = \text{length} \times \text{width} \]
Since each side of the park is 10 units long, the area is: \[ 10 \times 10 = 100 \text{ squares} \]
The exercise gives percentage requirements for various areas within the park, which must be converted into number of squares on the grid. To find these areas, multiply the total number of squares (100) by each percentage. This helps in visualizing the space allocation:

• Picnic Area: At least 12% \[ 0.12 \times 100 = 12 \text{ squares} \]
• Play Area: Between 15% and 30% \[0.15 \times 100 = 15 \text{ squares} \] to \[ 0.30 \times 100 = 30 \text{ squares} \], so the area must be between 15 and 30 squares.
• Goldfish Pond: No more than 10% \[ 0.10 \times 100 = 10 \text{ squares} \]

Allocating space effectively ensures the park meets community guidelines.

Percentage

Understanding percentages is crucial in this park planning exercise. Percentages represent parts per hundred and are commonly used in everyday calculations. In the context of the park, we need to allocate certain parts of the park as per the given percentages.
For example, to find out how much of the park should be a picnic area, we calculate 12% of the total area: \[0.12 \times 100 = 12 \text{ squares} \]
Similarly, for the play area, the range lies between 15% and 30%: \[ 0.15 \times 100 = 15 \text{ squares} \] to \[ 0.30 \times 100 = 30 \text{ squares} \] bullet
Finally, for the goldfish pond, a maximum of 10% is allowed, so: \[ 0.10 \times 100 = 10 \text{ squares} \]
These percentage calculations help us convert abstract guidelines into a concrete, visual plan that fits within the 100-square grid.

Geometry

Geometry plays a central role in planning the layout of the park. The park is a square, a basic geometric shape with equal sides and angles.
Understanding the geometry helps ensure we use the space efficiently and meet all the requirements. Geometric shapes are easier to divide into smaller regions, facilitating the implementation of the percentage guidelines.
By drawing a 10x10 square grid, we ensure that each unit fits into the required spaces. For instance:
* The picnic area, which must occupy at least 12 squares, can be represented as a 3x4 rectangle within the grid to satisfy the requirement.
* For the play area, you could choose a 5x3 rectangle or any other shape that fits between 15 and 30 squares.
* Finally, the goldfish pond, covering no more than 10 squares, could be represented as a 2x5 rectangle.
Geometry allows us to creatively and accurately fit various features into the overall park layout while meeting specific guidelines.