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katrin2010 [14]
2 years ago
6

Find the area. 5cm 3cm 4 cm

Mathematics
1 answer:
Ostrovityanka [42]2 years ago
6 0

Answer:

6 cm²

Step-by-step explanation:

Since 3 side lengths are given, I assume that this figure is a triangle. The area of a triangle can be determined by using hero's formula.

\text{Area of triangle} = \sqrt{\text{s(s - a)(s - b)(s - c)}

⇒ s = Perimeter/2

⇒ a, b, and c = side lenths of triangle

<u>Replacing a, b, and c as the given side lengths:</u>

\implies \text{Area of triangle} = \sqrt{\text{s(s - 5)(s - 3)(s - 4)}

<u>Determining the perimeter of the triangle:</u>

\text{Perimeter of triangle = Sum of it's side lengths}

\implies \text{Perimeter of triangle =}\ 5 + 4 + 3

\implies \text{Perimeter of triangle =}\ 12 \ \text{cm}

<u>Determining the half of perimeter:</u>

\text{Half of perimeter} = s = \dfrac{\text{Perimeter}}{2}

\implies s = \dfrac{12}{2}

\implies s = 6

<u>Replacing the value of "s" in the formula:</u>

\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}

<u>Evaluating the area:</u>

\implies \text{Area of triangle} = \sqrt{\text{6(6 - 5)(6 - 3)(6 - 4)}

\implies \text{Area of triangle} = \sqrt{\text{6(1)(3)(2)}

\implies \text{Area of triangle} = \sqrt{\text{6(6)}

\implies \text{Area of triangle} = 6 \ \text{cm}^{2}

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