Numeracy

Perimeter and Circumference




Perimeter and circumference measure the total distance around a 2D shape. While "perimeter" applies to all shapes, "circumference" is specific to circles. These calculations are vital for tasks ranging from geometry problems to real-life applications like fencing a garden or marking a sports field.

Perimeter of Polygons

  • Definition: The perimeter is the sum of the lengths of all sides of a polygon.
  • Unit: Measured in linear units (e.g., meters, inches).

Regular Polygons

For polygons where all sides are equal:
[
{Perimeter} = n * s
]
Where:
- (n) = Number of sides.
- (s) = Length of one side.

Example:
A square with a side length of 6m:
[
{Perimeter} = 4 * 6 = 24 \, {m}
]

Irregular Polygons

For shapes with unequal sides:
[
{Perimeter} = {Sum of all side lengths.}
]

Example:
A rectangular football pitch measuring 105m × 68m:
[
{Perimeter} = 2 * (105 + 68) = 2 * 173 = 346 \, {m.}
]

Circumference of Circles

  • Definition: The circumference is the perimeter of a circle.
  • Formula:
    [
    {Circumference} = 2\pi r \quad {or} \quad \pi D
    ]
    Where:
  • (r) = Radius.
  • (D) = Diameter ((D = 2r)).
  • (\pi \approx 3.142).

Example:
The radius of a center circle on a football field is 9.15m:
[ {Circumference} = 2\pi * 9.15 = 57.5 \, {m (rounded to one decimal place).} ]

Perimeter of Ellipses

  • Definition: An ellipse is an elongated or squashed circle.
  • Approximation Formula:
    [ p \approx 2\pi \sqrt{\frac{a^2 + b^2}{2}} ]
    Where:
  • (a) = Half the major axis (longest diameter).
  • (b) = Half the minor axis (shortest diameter).

Note: This formula is an approximation; accuracy decreases as the ellipse becomes more elongated.

Key Points to Remember

  1. Perimeter vs. Area:
  2. Perimeter measures the length around a shape.

  3. Area measures the space inside a shape.

  4. Units:

  5. Perimeter and circumference are in linear units (e.g., meters).

  6. Area is in square units (e.g., m²).

  7. Applications:

  8. Useful in professions like surveying, architecture, and sports ground maintenance.

  9. Everyday tasks include measuring fencing, painting, and landscaping.

  10. Tools:

  11. For short distances: Tape measures or measuring wheels.
  12. For long or complex distances: Electronic distance measurement (EDM) devices and theodolites.

With these formulas and examples, you can confidently calculate perimeters and circumferences for any shape, whether designing a project or solving geometry problems.?

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