If the three sides of a triangle are 6.00 feet, 8.00 feet, and 12.0 feet, what is the area of the triangle? Round the answer to 3 significant digits.
To find the area of a triangle, we can use Heron's formula.
Heron's formula states that the area of a triangle with sides lengths a, b, and c is given by:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c)/2
In this case, the sides of the triangle are 6.00 feet, 8.00 feet, and 12.0 feet.
The semiperimeter, s, is:
s = (6.00 + 8.00 + 12.0)/2 = 26.0/2 = 13.0
Now we can substitute the values into the formula:
Area = √(13.0(13.0-6.00)(13.0-8.00)(13.0-12.0))
= √(13.0(7.00)(5.00)(1.00))
= √(455.0)
= 21.34 feet²
Rounding to 3 significant digits, the area of the triangle is 21.34 feet².