NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Two-dimensional representations

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A craft designer in Melbourne is creating a decorative 2D representation of a three-dimensional wooden box used in a traditional Aboriginal art installation. The box is a rectangular prism with a length of 64 cm, a width of 40 cm, and a height of 16 cm.

The designer wants to draw the front view of the box on isometric grid paper, which shows the height and length in proportion, with the width foreshortened. In this front view, the face that shows the length and height is a rectangle.

What is the exact area, in square centimetres, of this two-dimensional front view?

Concept illustrations

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The front view of a rectangular prism shows the length and height dimensions. The width is foreshortened and not visible in the front view.
  2. The given length of the box is 64 cm and the height is 16 cm. These are the two dimensions that appear in the front view.
  3. The front view is a rectangle formed by the length and height. The area of a rectangle is calculated as length × height.
  4. Substitute the values: area = 64 cm × 16 cm.
  5. Perform the multiplication: 64 × 16 = 1024.
  6. Include the unit: 1024 cm².
  7. The front view is a 2D representation, so the area is simply the product of the visible length and height.
  8. No scaling or foreshortening adjustment is needed for area calculation because the front view is drawn to scale and shows length and height in proportion.
  9. The width (40 cm) does not affect the area of the front face, as it is not visible in this view.
  10. The area of the front view is exactly 1024 square centimetres.
  11. Check: 64 × 16 = (60 + 4) × 16 = 60×16 + 4×16 = 960 + 64 = 1024. Correct.
  12. The front view area is 1024 cm², which matches the calculated result.

Reference answer: 1024 cm²

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