NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Exploring formulas

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A community garden in Brisbane is being designed with a rectangular plot for vegetable beds. The length of the plot is fixed at 67 m, and the width is fixed at 24 m.

The formula for the area A of a rectangle is A = l × w.

What is the exact area of the garden plot in square metres?

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Replace x with its given value. For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.2x + 3x = 4→2 × 4 + 3Substitute→11Evaluate
For x = 4, the expression 2x + 3 becomes 2 × 4 + 3 = 11.
Keep both sides balanced. The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.x + 614−6−6x = 8
The level beam represents equality, not measured weights. Subtract 6 from both sides of x + 6 = 14 to leave x = 8.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The length l of the rectangular garden plot is given as 67 m, and the width w is 24 m.
  2. The formula for the area A of a rectangle is A = l × w.
  3. Substitute the given values into the formula: A = 67 × 24.
  4. Perform the multiplication: 67 × 24.
  5. Break down 24 as 20 + 4 to use the distributive property: 67 × (20 + 4) = (67 × 20) + (67 × 4).
  6. Calculate 67 × 20: 67 × 20 = 1340.
  7. Calculate 67 × 4: 67 × 4 = 268.
  8. Add the two products: 1340 + 268 = 1608.
  9. The area is 1608 square metres.
  10. Check the result by reversing the multiplication: 1608 ÷ 24 = 67, which matches the given length.
  11. The calculation is correct and consistent with the given dimensions.
  12. Therefore, the exact area of the garden plot is 1608 square metres.

Reference answer: 1608 m²

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