How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #5 #, and #5 #?
Here, we know that
which gives an area of
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To use Heron's formula to find the area of a triangle with sides of lengths ( a = 4 ), ( b = 5 ), and ( c = 5 ), follow these steps:
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Calculate the semi-perimeter of the triangle, denoted by ( s ), using the formula: [ s = \frac{a + b + c}{2} ]
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Compute the expression under the square root in Heron's formula, denoted by ( \Delta ), using the semi-perimeter calculated in step 1: [ \Delta = s(s - a)(s - b)(s - c) ]
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Take the square root of ( \Delta ) to find the area of the triangle: [ \text{Area} = \sqrt{\Delta} ]
Let's compute it:
Step 1: [ s = \frac{4 + 5 + 5}{2} = \frac{14}{2} = 7 ]
Step 2: [ \Delta = 7(7 - 4)(7 - 5)(7 - 5) ] [ = 7(3)(2)(2) = 84 ]
Step 3: [ \text{Area} = \sqrt{84} ]
Now, you can simplify ( \sqrt{84} ) to find the exact area of the triangle.
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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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- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #39 # and the height of the cylinder is #17 #. If the volume of the solid is #60 pi#, what is the area of the base of the cylinder?
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