NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Area of triangles and parallelograms

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Required skills (click to reveal)

A triangular section of a roof in Adelaide is to be covered with solar panels. The base of the triangle is 13/4 metres and the perpendicular height from the base to the opposite vertex is 5/2 metres.

Using the formula for the area of a triangle, calculate the exact area in square metres. Express your answer as a simplified fraction.

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Base and perpendicular height. Using base 4 and perpendicular height 3, area = ½ × 4 × 3 = 6 square units.345
Using base 4 and perpendicular height 3, area = ½ × 4 × 3 = 6 square units.

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Formula

Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The problem requires calculating the area of a triangle with base 13/4 metres and perpendicular height 5/2 metres. The area of a triangle is given by the formula: area = (1/2) × base × height.
  2. Substitute the given base and height into the formula: area = (1/2) × (13/4) × (5/2).
  3. Multiply the numerators: 1 × 13 × 5 = 65.
  4. Multiply the denominators: 2 × 4 × 2 = 16.
  5. The product is 65/16 square metres.
  6. Simplify the fraction 65/16. The greatest common divisor of 65 and 16 is 1, so the fraction is already in simplest form.
  7. The area is 65/16 square metres. This is an improper fraction, but it is already simplified.
  8. Check the calculation: (1/2) × (13/4) × (5/2) = (1 × 13 × 5) / (2 × 4 × 2) = 65/16. Correct.
  9. Verify units: base and height are in metres, so area is in square metres. Correct.
  10. The final area is 65/16 square metres, which is approximately 4.0625 m², but the exact value is required.
  11. The answer is a simplified fraction, as required.
  12. The exact area of the triangular roof section is 65/16 square metres.

Reference answer: 65/16

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