How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #6 #?

Answer 1

#\sqrt{(17/2)(3/2)(9/2)(5/2)}=(3/4)\sqrt{255}#

Let a, b, c be the sides of the triangle. Calculate the semi-perimeter s = (a+b+c)/2. Heron's formula for the area is

#\sqrt{s(s-a)(s-b)(s-c)}#
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Answer 2

To use Heron's formula to find the area of a triangle with sides of lengths (a), (b), and (c), where (s) is the semiperimeter (half of the perimeter), you follow these steps:

  1. Calculate the semiperimeter (s) using the formula: [s = \frac{a + b + c}{2}.]

  2. Then, use Heron's formula: [Area = \sqrt{s(s-a)(s-b)(s-c)}.]

For the given triangle with side lengths (a = 7), (b = 4), and (c = 6), we first find the semiperimeter (s): [s = \frac{7 + 4 + 6}{2} = \frac{17}{2} = 8.5.]

Now, plug the values into Heron's formula: [Area = \sqrt{8.5(8.5-7)(8.5-4)(8.5-6)}.]

[= \sqrt{8.5(1.5)(4.5)(2.5)}.]

[= \sqrt{8.5(1.5)(4.5)(2.5)}.]

[= \sqrt{229.6875}.]

[= 15.134.]

So, the area of the triangle is approximately (15.134) square units.

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Answer from HIX Tutor

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.

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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