Final answer:
To find the area of a triangle with side lengths 12m, 9m, and 15m using Heron's formula, calculate the semiperimeter and use it in the formula to find the area, which is 44m².
Step-by-step explanation:
To find the area of a triangle using Heron's formula, we need to know the lengths of all three sides. In this case, the lengths of the sides are given as 12m, 9m, and 15m. Heron's formula states that the area of a triangle is given by:
Area = √(s(s-a)(s-b)(s-c))
Where 'a', 'b', and 'c' are the lengths of the sides of the triangle, and 's' is the semiperimeter (half of the perimeter).
Let's calculate the area using this formula:
First, calculate the semiperimeter 's' by adding all the side lengths and dividing by 2: s = (12 + 9 + 15)/2 = 18
Now, plug these values into the formula to find the area:
Area = √(18(18-12)(18-9)(18-15)) = √(18*6*9*3) = √1944 = 44m²
Learn more about Finding the area of a triangle