To find the area of a triangular plot of land with sides measuring 5 meters, 7 meters, and 10 meters, we can use Heron's formula.
First, we calculate the semi-perimeter \( s \) of the triangle:
\[ s = \frac{a + b + c}{2} = \frac{5 + 7 + 10}{2} = \frac{22}{2} = 11 \text{ meters} \]
Next, we apply Heron's formula to find the area \( A \):
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substituting the values of \( a = 5 \), \( b = 7 \), and \( c = 10 \):
\[ A = \sqrt{11(11-5)(11-7)(11-10)} = \sqrt{11 \times 6 \times 4 \times 1} \]
Calculating the products step by step:
\[ A = \sqrt{11 \times 6 \times 4} = \sqrt{264} \]
Now we compute \( \sqrt{264} \):
\[ \sqrt{264} \approx 16.2481 \]
Rounding to the nearest tenth, the area of the triangular plot of land is:
\[ \boxed{16.2} \text{ square meters} \]
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