How do you use Heron's formula to find the area of a triangle with sides of lengths #5 #, #6 #, and #7 #?
Heron's formula is:
Substitute the known values into Heron's formula.
Simplify.
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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 given by (s = \frac{a + b + c}{2}), you can use the following steps:
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Calculate the semi-perimeter: [ s = \frac{a + b + c}{2} ]
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Compute the area using Heron's formula: [ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} ]
For the given triangle with side lengths 5, 6, and 7:
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Calculate the semi-perimeter: [ s = \frac{5 + 6 + 7}{2} = 9 ]
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Compute the area using Heron's formula: [ \text{Area} = \sqrt{9(9 - 5)(9 - 6)(9 - 7)} = \sqrt{9 \times 4 \times 3 \times 2} = \sqrt{216} ]
Thus, the area of the triangle is ( \sqrt{216} ) 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.
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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- Points P(1,0), Q(8,0) and R(3,4) are the vertices of a triangle. What is the area of this triangle?
- Two corners of an isosceles triangle are at #(6 ,3 )# and #(5 ,8 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?
- If a triangle has an hypotenuse that is 15.4 miles long and a base that is 6.3 miles long, what is the measure of the remaining side?

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