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Answer :
Answer:
$63,030.97
Step-by-step explanation:
You want the cost at $2200 per acre of a triangular piece of land with side lengths 1360 ft, 1850 ft, and 2430 ft.
Area
The area of the triangle can be found using Heron's formula:
A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2
Using the given lengths, we find the area to be ...
A = √(2820·1460·970·390) = √(1.55753676×10^12) ≈ 1248013.1249
At 43560 square feet per acre, this is about ...
(1248013.1249 ft²)/(43560 ft²/ac) ≈ 28.65044 ac
Cost
At $2200 per acre, the cost of the land is ...
(28.65044 ac) × ($2200/ac) ≈ $63,030.97
The land costs $63,030.97.
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Final answer:
The cost of the triangular lot is approximately $77,110.00, which is calculated using Heron's formula to find the area of the lot in square feet, converting that area to acres.
Explanation:
To calculate the cost of the triangular lot, we first need to find the area of the triangle using Heron's formula since we have the lengths of all three sides. Let's define the sides as a = 1360 feet, b = 1850 feet, and c = 2430 feet.
1. Calculate the semi-perimeter (s):
s = (a + b + c) / 2
2. Use Heron's formula to find the area (A):
A = √[s(s - a)(s - b)(s - c)]
A ≈ √[2820 × 1460 × 970 × 390]
A ≈ 1,526,137.08 square feet
3. Convert the area to acres:
1 acre = 43,560 square feet
4. Calculate the cost:
Cost = area in acres × price per acre
Therefore, the cost of the land is approximately $77,110.00.
