Okay, so I need to find the area of a triangle with sides 5, 5, and 6 units. Hmm, let's see. Since two sides are equal (5 and 5), this is an isosceles triangle. That might help in calculating the area. 

First, I remember that the area of a triangle can be calculated using Heron's formula when all three sides are known. Heron's formula says that the area is the square root of [s(s - a)(s - b)(s - c)], where 's' is the semi-perimeter. Let me try that approach.

So, the semi-perimeter 's' would be (5 + 5 + 6)/2. Let me compute that: 5 + 5 is 10, plus 6 is 16. Divided by 2 gives 8. So s = 8.

Now, plugging into Heron's formula: area = √[8(8 - 5)(8 - 5)(8 - 6)]. Let's compute each part. 8 - 5 is 3, and 8 - 6 is 2. So that becomes √[8 * 3 * 3 * 2]. Multiplying those numbers: 8 * 3 is 24, another 3 is 72, times 2 is 144. So the area is √144, which is 12. Wait, that seems straightforward. 

But wait, maybe there's another way to confirm this. Since it's an isosceles triangle, maybe I can find the height and then use the formula (base * height)/2. Let's try that method.

In an isosceles triangle with sides 5, 5, and 6, the base is 6 units. The two equal sides are 5 each. If I split the triangle into two right triangles by drawing a height from the apex to the base, each right triangle will have a base of 3 units (since the original base is 6, so half of that is 3), a hypotenuse of 5 units (the equal side), and the height as the other leg.

Using the Pythagorean theorem: height² + 3² = 5². So height² = 25 - 9 = 16. Therefore, height = 4 units. Then the area is (base * height)/2 = (6 * 4)/2 = 24/2 = 12. 

Okay, both methods give the same result, 12 square units. That seems solid. But let me just double-check if there's any mistake in the calculations. 

First method: s = 8. Then the terms are 8, 3, 3, 2. Multiplying all together: 8*3=24, 24*3=72, 72*2=144. Square root of 144 is 12. Correct.

Second method: height calculation. Half the base is 3. Then 5² - 3² = 25 - 9 = 16. Square root is 4. Area is (6*4)/2 = 12. Both confirm the area is 12. 

I think that's it. The answer should be 12.
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