To calculate the area, we first need to understand what kind of shape we are dealing with given the dimensions you provided: 16 ft, 14 ft, and 12 ft. These dimensions suggest that it might be a triangle.
Assuming these dimensions are the lengths of the sides of a triangle, we can use Heron's formula to find the area. Heron's formula states:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
where \(s\) is the semi-perimeter of the triangle, and \(a\), \(b\), and \(c\) are the lengths of the sides of the triangle.
- First, calculate the semi-perimeter \(s\):
\[ s = \frac{a + b + c}{2} = \frac{16 + 14 + 12}{2} = \frac{42}{2} = 21 \text{ ft} \]
- Now, substitute the values into Heron's formula:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substituting \(s\), \(a = 16\), \(b = 14\), and \(c = 12\):
\[ A = \sqrt{21(21-16)(21-14)(21-12)} \] \[ A = \sqrt{21(5)(7)(9)} \] \[ A = \sqrt{21 \times 5 \times 7 \times 9} \]
Now we calculate the multiplication step-by-step:
- \(5 \times 7 = 35\)
- \(35 \times 9 = 315\)
- \(21 \times 315 = 6615\)
Now calculate the square root:
\[ A = \sqrt{6615} \]
To compute \(\sqrt{6615}\):
\[ \sqrt{6615} \approx 81.3 \]
Thus, the area of the triangle is approximately:
\[ A \approx 81.3 \text{ ft}^2 \]
So the final result is:
\[ a \approx 81.3 \text{ ft}^2 \]