Land in downtown Columbia is valued at $20 a square foot. What is the value of a triangular lot with sides of lengths 126, 144, and 186 ft? (Round your answer to the nearest dollar.)
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To find the value of the triangular lot, we need to calculate its area first.
Using Heron's formula, we can calculate the area of a triangle with sides a, b, and c as follows:
s = (a + b + c) / 2
area = √(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter.
In this case, the sides of the triangle are 126 ft, 144 ft, and 186 ft.
s = (126 + 144 + 186) / 2 = 228
area = √(228 * (228 - 126) * (228 - 144) * (228 - 186))
area ≈ 10260.52 square feet
To find the value of the triangular lot, we can multiply the area by the value per square foot:
value = area * value_per_square_foot
In this case, the value per square foot is $20.
value = 10260.52 * 20
value ≈ $205,210
Therefore, the value of the triangular lot is approximately $205,210.
To find the value of the triangular lot, we first need to find its area. We can use Heron's formula to find the area of a triangle given the lengths of its sides.
Heron's formula states that the area (A) of a triangle with sides of lengths a, b, and c is given by:
A = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, calculated as half of the sum of the lengths of its sides:
s = (a + b + c) / 2
In this case, the lengths of the sides are 126 ft, 144 ft, and 186 ft. Let's substitute these values into the formula to find the area:
s = (126 + 144 + 186) / 2 = 228
A = √(228(228-126)(228-144)(228-186))
Let's calculate this:
A = √(228 * 102 * 84 * 42)
A ≈ √(22,142,112)
To round the answer to the nearest dollar, we need to find the value of the land by multiplying the area of the triangular lot by the value per square foot:
Value = A * $20
Let's substitute the calculated value of the area into this formula:
Value ≈ √22,142,112 * $20
Now, let's calculate this using a calculator:
Value ≈ $4,705.16
Therefore, the value of the triangular lot is approximately $4,705 to the nearest dollar.