# How do you use Heron's formula to find the area of a triangle with sides of lengths #6 #, #6 #, and #7 #?

According to Heron's formula, the area of any triangle is equal to:

Thus, the region is:

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Archimedes' Theorem is a modern form of Heron's Formula. We set

Archimedes' Theorem is usually superior to Heron's Formula.

No semiperimeter, no multiple square roots when given coordinates.

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To use Heron's formula to find the area of a triangle with side lengths (a), (b), and (c), where (s) is the semi-perimeter, you first calculate (s) using the formula:

[s = \frac{a + b + c}{2}]

Then, you can use Heron's formula to find the area (A) of the triangle:

[A = \sqrt{s(s - a)(s - b)(s - c)}]

For the given triangle with side lengths (a = 6), (b = 6), and (c = 7), we first calculate (s):

[s = \frac{6 + 6 + 7}{2} = \frac{19}{2}]

Then, we substitute (s) and the side lengths into Heron's formula:

[A = \sqrt{\frac{19}{2} \left(\frac{19}{2} - 6\right) \left(\frac{19}{2} - 6\right) \left(\frac{19}{2} - 7\right)}]

[= \sqrt{\frac{19}{2} \times \frac{7}{2} \times \frac{7}{2} \times \frac{5}{2}}]

[= \sqrt{\frac{19 \times 7 \times 7 \times 5}{2 \times 2 \times 2 \times 2}}]

[= \sqrt{\frac{9315}{16}}]

Now, you can simplify the square root if possible:

[A \approx \sqrt{582.1875}]

Finally, you find the square root:

[A \approx 24.1406]

So, the area of the triangle with side lengths 6, 6, and 7 is approximately 24.1406 square units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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