High School

A triangular building is bounded by three streets. The building measures approximately 97 feet on the first street, 196 feet on the second street, and 173 feet on the third street.

Approximate the ground area covered by the building.

A = ___ sq ft

Round to the nearest hundredth.

Answer :

Final answer:

We calculate the area of the triangular building by using Heron's formula. The semi-perimeter 's' is first calculated, and then substituted into Heron's formula with the given sides of the triangle. The resulting area is approximately 8396.06 sqft.

Explanation:

The calculation of the approximate area of a triangular building involves using Heron's formula. Heron's formula allows you to calculate the area of a triangle when you know all three sides. Since we know that the building measures 97 feet, 196 feet, and 173 feet on the three respective sides, we can use Heron's formula, which is Area = sqrt[s(s - a)(s - b)(s - c)], where 's' is the semi-perimeter of the triangle and 'a', 'b', 'c' are the sides of the triangle.

First, calculate 's'.

s = (a+b+c) / 2

Substituting the given values for 'a', 'b', and 'c':

s = (97+196+173) / 2 = 233

Then, substitute 's', 'a', 'b', and 'c' into Heron's formula to get the area:

Area = sqrt[233(233 - 97)(233 - 196)(233 - 173)]

Approximately, the Area works out to be 8396.06 sqft, rounded to the nearest hundredth.

Learn more about Heron's formula here:

https://brainly.com/question/34150930

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