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Activity Discussion Math Heron’s Formula

  • 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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