Find the area of a triangle with side lengths of 5, 10, and 12.
To find the area of a triangle when the lengths of its three sides are known, you can use Heron's formula. This formula states that the area of a triangle is equal to the square root of (s*(s-a)*(s-b)*(s-c)) where a, b, and c are the side lengths of the triangle, and s is the semiperimeter (half the perimeter) of the triangle. 

In the case of the given triangle with side lengths 5, 10, and 12, let’s first find the semiperimeter:
s = (a + b + c) / 2
s = (5 + 10 + 12) / 2
s = 27 / 2
s = 13.5

Now substitute the side lengths and the semiperimeter into Heron’s formula as follows
Area = √(s * (s-a) * (s-b) * (s-c))
Area = √(13.5 * (13.5-5) * (13.5-10) * (13.5-12))
Area = √(13.5 * 8.5 * 3.5 * 1.5)
Area = 24.5446

So, the area of the triangle with side lengths of 5, 10, and 12 is approximately 24.5446 square units.
Complete the following task based on the instruction and optional input provided.### Instruction:
Find the area of a triangle with side lengths of 5, 10, and 12.

### Output:
To find the area of a triangle when the lengths of its three sides are known, you can use Heron's formula. This formula states that the area of a triangle is equal to the square root of (s*(s-a)*(s-b)*(s-c)) where a, b, and c are the side lengths of the triangle, and s is the semiperimeter (half the perimeter) of the triangle. 

In the case of the given triangle with side lengths 5, 10, and 12, let’s first find the semiperimeter:
s = (a + b + c) / 2
s = (5 + 10 + 12) / 2
s = 27 / 2
s = 13.5

Now substitute the side lengths and the semiperimeter into Heron’s formula as follows
Area = √(s * (s-a) * (s-b) * (s-c))
Area = √(13.5 * (13.5-5) * (13.5-10) * (13.5-12))
Area = √(13.5 * 8.5 * 3.5 * 1.5)
Area = 24.5446

So, the area of the triangle with side lengths of 5, 10, and 12 is approximately 24.5446 square units.