Question

A triangular building is bounded by three streets. The building measures approximately 83 feet on the first​ street, 189 feet on the second​ street, and 178 feet on the third street. Approximate the ground area K covered by the building.

Answer 1

To approximate the ground area covered by the triangular building, we can use Heron's formula. The area ≈ 5884.88 square feet.

Step-by-step explanation:

To approximate the ground area covered by the triangular building, we can use Heron's formula. Heron's formula states that the area of a triangle can be calculated using the lengths of its three sides. The formula is:

Area = sqrt(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle and a, b, and c are the lengths of the sides.

First, we need to calculate the semiperimeter, which is half the sum of the lengths of the three sides:

s = (83 + 189 + 178) / 2 = 225

Using the given lengths of the sides, we can now calculate the area:

Area = sqrt(225(225-83)(225-189)(225-178))

Area ≈ 5884.88 square feet

Answer 2

For this case we use Heron's formula to calculate the area of the building.
We have then:
A = root ((s) * (s-a) * (s-b) * (s-c))
Where,
s = (a + b + c) / 2
Substituting values:
s = (83 + 189 + 178) / 2
s = 225 feet
A = root ((225) * (225-83) * (225-189) * (225-178))
A = 7352.509776 feet ^ 2
Rounding off we have:
A = 7353 feet ^ 2
Answer:
The ground area K covered by the building is:
K = 7353 feet ^ 2