How do you use Heron's formula to find the area of a triangle with sides of lengths #18 #, #7 #, and #19 #?

Answer 1

#Area=62.9285# square units

Heron's formula for finding area of the triangle is given by #Area=sqrt(s(s-a)(s-b)(s-c))#
Where #s# is the semi perimeter and is defined as #s=(a+b+c)/2#
and #a, b, c# are the lengths of the three sides of the triangle.
Here let #a=18, b=7# and #c=19#
#implies s=(18+7+19)/2=44/2=22#
#implies s=22#
#implies s-a=22-18=4, s-b=22-7=15 and s-c=22-19=3# #implies s-a=4, s-b=15 and s-c=3#
#implies Area=sqrt(22*4*15*3)=sqrt3960=62.9285# square units
#implies Area=62.9285# square units
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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 semi-perimeter of the triangle (defined as (s = \frac{a + b + c}{2})), follow these steps:

  1. Calculate the semi-perimeter (s) using the formula (s = \frac{a + b + c}{2}).
  2. Use Heron's formula: Area ((A)) = (\sqrt{s(s - a)(s - b)(s - c)}).
  3. Substitute the values of (a), (b), and (c) into the formula.

Given the side lengths (a = 18), (b = 7), and (c = 19):

  1. Calculate the semi-perimeter (s) as (s = \frac{18 + 7 + 19}{2} = \frac{44}{2} = 22).
  2. Use Heron's formula: (A = \sqrt{22(22 - 18)(22 - 7)(22 - 19)}).
  3. Perform the calculation:

[ A = \sqrt{22(22 - 18)(22 - 7)(22 - 19)} ] [ A = \sqrt{22(4)(15)(3)} ] [ A = \sqrt{22 \times 4 \times 15 \times 3} ] [ A = \sqrt{3960} ]

So, the area of the triangle is (A = \sqrt{3960}).

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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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