How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 4 units in length?
Area ≈ 7.94
This procedure has two steps.
Step 1: Determine half of the triangle's perimeter (s).
Secondly, compute the area (A).
Assume a = 6, b = 4, and c = 4.
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To use Heron's formula to determine the area of a triangle with sides of lengths 6, 4, and 4 units, follow these steps:

Calculate the semiperimeter ((s)) of the triangle using the formula: [ s = \frac{a + b + c}{2} ] where (a), (b), and (c) are the lengths of the sides of the triangle.

Compute the expression inside the square root of Heron's formula: [ A = \sqrt{s(s  a)(s  b)(s  c)} ] where (s) is the semiperimeter, and (a), (b), and (c) are the lengths of the sides of the triangle.

Substitute the given side lengths (a = 6), (b = 4), and (c = 4) into the formulas.

Calculate the semiperimeter: [ s = \frac{6 + 4 + 4}{2} = 7 ]

Compute the expression inside the square root: [ A = \sqrt{7(7  6)(7  4)(7  4)} ] [ A = \sqrt{7(1)(3)(3)} ] [ A = \sqrt{63} ]

Simplify the square root: [ A = \sqrt{9 \times 7} ] [ A = 3\sqrt{7} ]
Therefore, the area of the triangle is (3\sqrt{7}) square units.
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When evaluating a onesided 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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