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Find the area of a triangle with legs that are 16 m, 12 m, and 8 m.

A. 16.4 m²
B. 54 m²
C. 46.5 m²
D. 38.2 m²

Answer :

The area of the triangle with side lengths 16 m, 12 m, and 8 m is approximately 46.5 m², calculated using Heron's formula with a semi-perimeter of 18 m. Thus, the correct answer is C.

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. Let [tex]\( a = 16 \, \text{m} \), \( b = 12 \, \text{m} \), and \( c = 8 \, \text{m} \)[/tex] be the lengths of the sides of the triangle.

Heron's formula states that the area [tex](\( A \))[/tex] of a triangle with sides of lengths [tex]\( a \), \( b \), and \( c \)[/tex] can be calculated using the semi-perimeter [tex]\( s \)[/tex]:

[tex]\[ s = \frac{a + b + c}{2} \][/tex]

[tex]\[ A = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

First, calculate the semi-perimeter \( s \):

[tex]\[ s = \frac{16 + 12 + 8}{2} = 18 \, \text{m} \][/tex]

Now, plug the values into Heron's formula:

[tex]\[ A = \sqrt{18(18 - 16)(18 - 12)(18 - 8)} \][/tex]

[tex]\[ A = \sqrt{18 \times 2 \times 6 \times 10} \][/tex]

[tex]\[ A = \sqrt{2160} \][/tex]

[tex]\[ A \approx 46.5 \, \text{m}^2 \][/tex]

So, the correct answer is option C: [tex]\( 46.5 \, \text{m}^2 \)[/tex].

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Rewritten by : Jeany

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