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In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of tr

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Question: In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of triangle DEF?

Options:

  1. 24 cm²
  2. 30 cm²
  3. 48 cm²
  4. 60 cm²

Correct Answer: 30 cm²

Solution: 

Using Heron\'s formula, the semi-perimeter s = (6 + 8 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12*6*4*2] = √576 = 24 cm².

In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of tr

Practice Questions

Q1
In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of triangle DEF?
  1. 24 cm²
  2. 30 cm²
  3. 48 cm²
  4. 60 cm²

Questions & Step-by-Step Solutions

In triangle DEF, if DE = 6 cm, DF = 8 cm, and EF = 10 cm, what is the area of triangle DEF?
  • Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
  • Semi-perimeter – The semi-perimeter of a triangle is half the sum of its side lengths, used in Heron's formula.
  • Triangle Inequality Theorem – A principle that states the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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