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

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A triangular prism has a triangular base with side lengths of 5 cm, 5 cm and 6 cm. When viewed from the front, the two-dimensional representation of the prism shows a rectangle with a height of 8 cm and a width equal to the base of the triangle.

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

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The front view of the triangular prism is a rectangle. The width of this rectangle is equal to the base of the triangular base, which is 6 cm.
  2. The height of the rectangle is given as 8 cm, which corresponds to the height of the prism.
  3. The area of a rectangle is calculated using the formula: area = width × height.
  4. Substitute the given values: width = 6 cm, height = 8 cm.
  5. Perform the multiplication: 6 × 8 = 48.
  6. The result is in square centimetres (cm²), as area is a two-dimensional measurement.
  7. The front view is a rectangle with dimensions 6 cm by 8 cm, so its area is 48 cm².
  8. No further calculations are needed because the front view is explicitly described as a rectangle with known width and height.
  9. The area of the front view is exactly 48 cm².
  10. Check: 6 cm × 8 cm = 48 cm². This matches the expected area.
  11. The front view is a 2D representation of the prism's side face, and since the base is 6 cm and height is 8 cm, the area is correctly calculated.
  12. The exact area of the two-dimensional front view is 48 square centimetres.

Reference answer: 48 cm²

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