Question

a triangular building is bounded by three streets. the building measures approximately 81 feet on the first street, 183 feet on the second street, and 176 feet on the third street. approximate the ground area a covered by the building.
a≈□ square feet
(round to the nearest hundredth as needed.)

Explanation:

Step1: Identify the formula for the area of a triangle using Heron's formula.

Heron's formula for the area of a triangle with sides \(a\), \(b\), and \(c\) is \(A = \sqrt{s(s - a)(s - b)(s - c)}\), where \(s=\frac{a + b + c}{2}\) (the semi - perimeter). Let \(a = 81\), \(b = 183\), and \(c = 176\).

Step2: Calculate the semi - perimeter \(s\).

$$
LATEXBLOCK0
$$

Step3: Calculate the area \(A\) using Heron's formula.

$$
LATEXBLOCK1
$$

Answer:

\(7055.79\)