To solve the problem of calculating the area of a triangle with side lengths 5, 12, and 13, follow these steps:

Step 1: Identify if it's a right triangle

Check if the Pythagorean theorem holds:
[5^2 + 12^2 = 25 + 144 = 169 = 13^2]
Yes, this is a right-angled triangle with legs 5 and 12 (the two shorter sides), and hypotenuse 13.

Step 2: Calculate the area

The area of a right triangle is given by:
[Area = \frac{1}{2} \times base \times height]
Using the legs as base and height:
[Area = \frac{1}{2} \times 5 \times 12 = 30]

Answer: 30.

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