A triangular parcel of land has borders of lengths 55 meters, 85 meters, and 100 meters. Find the area of the parcel of land.
pick any angle (say, A) and find it via
a^2 = b^2 + c^2 - 2bc cosA
Now the area is given by 1/2 bc sinA
checking for right-angled triangle:
is 100^2 = 55^2 + 85^2 ?
NO
so let's find the smallest angle by the cosine law:
55^2 = 100^2 + 85^2 - 2(100)(85)cosØ
cosØ = 14200/17000 = .83529..
Ø = 33.35..° , (I stored it for accuracy on my calculator
So area = (1/2)(85)(100)sin 33.35..° = appr 2336.66
or using Heron's formula
s = (1/2)(100+85+55) = 120
s-a = 120-100 = 20
s-b = 120 - 85 = 35
s-c = 120-55 = 65
area = √(120*20*35*65) = appr 2336.66
To find the area of a triangular parcel of land, we can use Heron's formula, which states:
Area = √(s(s-a)(s-b)(s-c))
Where s is the semi-perimeter (half of the perimeter) of the triangle, and a, b, and c are the lengths of the sides of the triangle.
In this case, the lengths of the sides of the triangular parcel of land are 55 meters, 85 meters, and 100 meters.
The semi-perimeter, s, is calculated by:
s = (a + b + c) / 2
Plugging in the values:
s = (55 + 85 + 100) / 2
s = 240 / 2
s = 120
Now we can calculate the area using Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
Area = √(120(120-55)(120-85)(120-100))
Simplifying the expression:
Area = √(120(65)(35)(20))
Area = √(120 * 45500)
Area = √5460000
Area ≈ 233.54 square meters
Therefore, the area of the triangular parcel of land is approximately 233.54 square meters.
To find the area of a triangular parcel of land, we can use the Heron's formula.
Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = √(s(s - a)(s - b)(s - c))
where s is the semiperimeter, calculated using the formula:
s = (a + b + c) / 2
Let's apply this formula to find the area of the triangular parcel of land with side lengths 55 meters, 85 meters, and 100 meters.
Step 1: Calculate the semiperimeter (s):
s = (55 + 85 + 100) / 2
s = 240 / 2
s = 120 meters
Step 2: Use Heron's formula to find the area:
Area = √(s(s - a)(s - b)(s - c))
Area = √(120(120 - 55)(120 - 85)(120 - 100))
Area = √(120 * 65 * 35 * 20)
Area = √(109200000)
Area ≈ 3306.8 square meters
Therefore, the area of the parcel of land is approximately 3306.8 square meters.