The triangle with length sides of 5,12, and 13 is a right triangle because `5^2 + 12^2 = 13^2.`

In a right triangle, the 2 legs represent the base and height of the triangle. Therefore the height and base each have lengths 5 and 12.

In order to find the area of a triangle, use the formula:

`A = 1/2bh`

Using this, `A = 1/2*5*12`

`A = 1/2*60`

`A = 30`

**Therefore, the area of a triangle with sides 5,12, and 13 is:`30 units^2`**

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The length of the sides of the triangle are 5, 12 and 13. It should be noticed that 5^2 + 12^2 = 25 + 144 = 169 = 13^2. As a result the given triangle is a right triangle with base and height 5 and 12 resp.

The area of a triangle with base b and height h is A = (1/2)*b*h. Substituting the values of b = 5 and h = 12 gives A = 30.

**A triangle with sides 5. 12 and 13 has an area 30 square units.**