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, which is given by:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
where \(s\) is the semi-perimeter of the triangle, and \(a\), \(b\), and \(c\) are the lengths of the sides.
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First, calculate the semi-perimeter \(s\): \[ s = \frac{a + b + c}{2} = \frac{5 + 7 + 10}{2} = \frac{22}{2} = 11 \text{ meters} \]
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Now, apply Heron's formula: \[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
Substitute the values: \[ A = \sqrt{11(11-5)(11-7)(11-10)} \] \[ A = \sqrt{11 \times 6 \times 4 \times 1} \] \[ A = \sqrt{11 \times 24} \] \[ A = \sqrt{264} \] Calculating the square root: \[ A \approx 16.248 \]
To the nearest tenth, the area of the triangular plot of land is approximately 16.2 square meters.
Thus, the answer is: 16.2 sq meters
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