A triangle has sides measuring 5 cm, 12 cm, and 13 cm. What is its area?

To find the area of a triangle when you know the lengths of all three sides, you can use Heron's formula. First, calculate the semi-perimeter (s) of the triangle, which is the sum of the lengths of its sides divided by 2:

[

s = \frac{a + b + c}{2} = \frac{5 + 12 + 13}{2} = 15 , \text{cm}

]

Next, you apply Heron's formula, which is:

[

Area = \sqrt{s(s-a)(s-b)(s-c)}

]

Now substituting in our values, where (a = 5) cm, (b = 12) cm, and (c = 13) cm:

[

Area = \sqrt{15(15-5)(15-12)(15-13)}

]

Calculating each term inside the square root:

[

Area = \sqrt{15 \times 10 \times 3 \times 2} = \sqrt{15 \times 60} = \sqrt{900} = 30 , \text{cm}^2

]

Thus, the area of the