Answer:
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)
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)
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
A≈106466.25A≈106466.25
A≈326.58 yd2A≈326.58yd2
So, the area of the triangular field is approximately 326.58326.58 square yards.