Determine the area of a triangle if the three sides of the triangle are 5.0 feet, 7.5 feet, and 9.0 feet. Round the answer to 4 significant digits.
Using Heron's formula, the area (A) of a triangle with side lengths a, b, and c is given by:
A = √(s(s - a)(s - b)(s - c))
where s is the semiperimeter of the triangle. The semiperimeter (s) is given by:
s = (a + b + c) / 2
Plugging in the given values, we have:
s = (5.0 + 7.5 + 9.0) / 2 = 21.5 / 2 = 10.75 feet
Now, we can calculate the area:
A = √(10.75(10.75 - 5.0)(10.75 - 7.5)(10.75 - 9.0))
A ≈ √(10.75(5.75)(3.25)(1.75))
A ≈ √(125.3990625)
A ≈ 11.19
Rounding to 4 significant digits, the area of the triangle is 11.19 square feet.