Question

A triangular field has sides of lengths 29, 55, 77 yd.

Enter your answer as a number; answer should be accurate to 2 decimal places.

Answer 1

Step-by-step explanation:

To find the area of a triangular field given the lengths of its sides (a, b, c) using Heron's formula, you can use the following steps:

Calculate the semi-perimeter (ss) of the triangle using the formula:

s=a+b+c2s=2a+b+c​

Calculate the area (AA) using Heron's formula:

A=s⋅(s−a)⋅(s−b)⋅(s−c)A=s⋅(s−a)⋅(s−b)⋅(s−c)

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Given that the sides of the triangular field are a=29 yda=29yd, b=55 ydb=55yd, and c=77 ydc=77yd, we can proceed with the calculations:

s=29+55+772s=229+55+77​

s=1612s=2161​

s=80.5s=80.5

Now, substitute this value into Heron's formula:

A=80.5⋅(80.5−29)⋅(80.5−55)⋅(80.5−77)A=80.5⋅(80.5−29)⋅(80.5−55)⋅(80.5−77)

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Calculate the expression inside the square root, and then take the square root of the result to get the area.

A≈80.5⋅51.5⋅25.5⋅3.5A≈80.5⋅51.5⋅25.5⋅3.5

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A≈106466.25A≈106466.25

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A≈326.58 yd2A≈326.58yd2

So, the area of the triangular field is approximately 326.58326.58 square yards.