What is the area of a triangle if the three sides of a triangle are 9.00 feet, 11.00 feet, and 14.00 feet. Round the answer to 3 significant digits.
To find the area of the triangle, we can use Heron's formula:
s = (a + b + c) / 2
where a, b, and c are the lengths of the three sides of the triangle.
In this case:
a = 9.00 feet
b = 11.00 feet
c = 14.00 feet
s = (9.00 + 11.00 + 14.00) / 2
s = 17.00
Now we can use Heron's formula to find the area:
Area = √[s(s - a)(s - b)(s - c)]
Area = √[17(17 - 9)(17 - 11)(17 - 14)]
Area = √[17(8)(6)(3)]
Area = √[2448]
Area ≈ 49.479 feet²
Therefore, the area of the triangle is approximately 49.5 feet².