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Answer :
Final answer:
The area of the triangle can be found using the Heron's formula.
the area of the triangle is 54m², which is option a.
Explanation:
To find the area of a triangle, we can use the formula for the area of a triangle with given side lengths - the Heron's formula. Let's call the lengths of the legs of the triangle a, b, and c. The formula for the area of a triangle using Heron's formula is:
A = sqrt(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle calculated as s = (a + b + c) / 2. In this case, a = 12m, b = 15m, and c = 9m. Substituting the values into the formula, we get:
A = sqrt(s(s-a)(s-b)(s-c))
= sqrt((18m)(6m)(3m)(9m))
= sqrt(2916m²)
= 54m²
Therefore, the area of the triangle is 54m², which is option a.
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