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How do you use Heron's formula to find the area of a triangle with sides of lengths #5 #, #5 #, and #5 #?

Answer 1

Sophia Alfred

The Area is #10.825 units^2#

First we would find S which is the sum of the 3 sides divided by 2.

#S = (5 + 5 + 5)/2 # = #15/2# = 7.5

Then use Heron's Equation to calculate the area.

#Area = sqrt(S(S-A)(S-B)(S-C)) #

#Area = sqrt(7.5(7.5-5)(7.5-5)(7.5-5)) #

#Area = sqrt(7.5(2.5)(2.5)(2.5)) #

#Area = sqrt(117.1875) #

#Area = 10.825 units^2 #

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Answer 2

Evelyn Arboleda

Using Heron's formula, the area ((A)) of a triangle with side lengths (a), (b), and (c) is calculated using the semi-perimeter (s) and the formula:

[ A = \sqrt{s(s - a)(s - b)(s - c)} ]

Where ( s = \frac{a + b + c}{2} ) is the semi-perimeter.

For the given triangle with side lengths 5, 5, and 5, the semi-perimeter is:

[ s = \frac{5 + 5 + 5}{2} = \frac{15}{2} = 7.5 ]

Substituting (a = 5), (b = 5), (c = 5), and (s = 7.5) into Heron's formula:

[ A = \sqrt{7.5(7.5 - 5)(7.5 - 5)(7.5 - 5)} ]

[ A = \sqrt{7.5 \times 2.5 \times 2.5 \times 2.5} ]

[ A = \sqrt{7.5 \times 15.625} ]

[ A = \sqrt{117.1875} ]

[ A \approx 10.82 ]

The area of the triangle is approximately 10.82 square units.

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