Question

Find the area.
a = [?]ft²
16 ft, 12 ft and 14 ft
JUST FIGURE IT OUT RIGHT!

Answer 1

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:

1. **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.

2. **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:

\[
21 \times 5 = 105
\]
\[
9 \times 7 = 63
\]
\[
105 \times 63 = 6615
\]

3. **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:

\[
\text{Area } a \approx 81.3 \text{ ft²}
\]