• Math

  Heron’s Formula

  Posted by Nitesh on February 2, 2024 at 4:27 pm

  Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42cm.

  brajesh replied 2 months ago 2 Members · 1 Reply

  • Heron's Formula
• 1 Reply

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  brajesh

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  February 24, 2024 at 10:46 am

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  To find the area of a triangle when two sides and the perimeter are known, we can use Heron’s formula. Heron’s formula states that the area (A) of a triangle with sides a, b, and c can be calculated using the semi-perimeter (s) as follows:

  A = √(s(s-a)(s-b)(s-c))

  where s = (a + b + c) / 2.

  In this case, the two sides given are 18 cm and 10 cm, and the perimeter is 42 cm. Let’s calculate the area:

  s = (a + b + c) / 2 = (18 + 10 + c) / 2 = (28 + c) / 2 = 14 + c/2

  Since the perimeter is 42 cm, we have:

  42 = 18 + 10 + c
  42 = 28 + c
  c = 42 – 28
  c = 14 cm

  Now we can substitute the values of a, b, and c into Heron’s formula:

  s = (18 + 10 + 14) / 2 = 42 / 2 = 21

  A = √(21(21-18)(21-10)(21-14))
  = √(21(3)(11)(7))
  = √(21311*7)
  = √(5397)
  ≈ 73.49 cm²

  Therefore, the area of the triangle is approximately 73.49 square centimeters.

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