To find the area of a triangle with sides measuring 16 ft, 12 ft, and 14 ft, we can use Heron's formula. Here are the steps:
-
Calculate the semi-perimeter (s):
\[ s = \frac{a + b + c}{2} = \frac{16 + 12 + 14}{2} = \frac{42}{2} = 21 \text{ ft} \]
where \(a = 16\) ft, \(b = 12\) ft, and \(c = 14\) ft.
-
Calculate the area (A) using Heron's formula:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Plugging in the values:
\[ A = \sqrt{21 \times (21 - 16) \times (21 - 12) \times (21 - 14)} \]
Simplifying the terms inside the square root:
\[ A = \sqrt{21 \times 5 \times 9 \times 7} \]
Now calculating it step by step:
\[ 21 \times 5 = 105 \] \[ 9 \times 7 = 63 \] \[ 105 \times 63 = 6615 \]
-
Taking the square root:
\[ A = \sqrt{6615} \]
To find \( \sqrt{6615} \):
\( \sqrt{6615} \approx 81.3 \)
So, the area of the triangle is approximately 81.3 ft².
Final answer:
\[ \text{Area } a \approx 81.3 \text{ ft²} \]