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

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A sports equipment manufacturer in Brisbane is designing a new storage box for footballs and rugby balls. The box is in the shape of a rectangular prism with a length of 22 cm, a width of 14 cm, and a height of 61 cm.

When viewed from the front (looking at the 22 cm by 61 cm face), the two-dimensional representation shows a rectangle.

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

Concept illustrations

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The front view of the rectangular prism is the face with dimensions length (22 cm) and height (61 cm). This is given as the front-facing rectangle.
  2. The area of a rectangle is calculated using the formula: area = length × width.
  3. Substitute the given values: length = 22 cm, height = 61 cm. The width in this view is the height of the prism.
  4. Calculate: 22 × 61. Break it down using distributive property: 22 × (60 + 1) = (22 × 60) + (22 × 1).
  5. Compute 22 × 60: 22 × 6 × 10 = 132 × 10 = 1320.
  6. Compute 22 × 1 = 22.
  7. Add the two parts: 1320 + 22 = 1342.
  8. The area is 1342 square centimetres.
  9. Verify by direct multiplication: 22 × 61 = 1342. Correct.
  10. The front view is a 2D representation of the 22 cm by 61 cm face, so the area is exactly 1342 cm².
  11. The question asks for the exact area of the front view, which is 1342 cm².
  12. Final answer confirmed: 1342 cm².

Reference answer: 1342 cm²

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