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The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

Correct answer: D. None of these

  • A. 25 cm2
  • B. 42 cm2
  • C. 49 cm2
  • D. None of these

Explanation

For any triangle, area = inradius x semiperimeter. The semiperimeter is 28 cm ÷ 2 = 14 cm, so the area is 2.5 cm x 14 cm = 35 cm2, which is not listed. The likely mistake is option a, which may come from multiplying the inradius by the full perimeter instead of the semiperimeter.

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Triangles and angles involve angle pairs, vertically opposite angles, parallel lines, triangle angle sums, exterior angles, congruence, similarity, and the Pythagorean theorem. Questions also test properties of isosceles and equilateral triangles, with similarity focusing on proportional sides while congruence requires identical size and shape.

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