Use an appropriate area formula to find the area of the triangle with the given side lengths. \( \begin{array}{l}a=17 \mathrm{~m} \\ b=10 \mathrm{~m} \\ \mathrm{c}=8 \mathrm{~m}\end{array} \) The area of the triangle is \( \square \mathrm{m}^{2} \). (Round your answer to the nearest tenth.)

To find the area of a triangle given its side lengths, we can use Heron's formula. First, we need to calculate the semi-perimeter \( s \) of the triangle: \[ s = \frac{a + b + c}{2} \] Substituting the given side lengths \( a = 17 \, \text{m} \), \( b = 10 \, \text{m} \), and \( c = 8 \, \text{m} \): \[ s = \frac{17 + 10 + 8}{2} = \frac{35}{2} = 17.5 \, \text{m} \] Next, we can use Heron's formula to find the area \( A \): \[ A = \sqrt{s(s-a)(s-b)(s-c)} \] Now we calculate each term: \[ s - a = 17.5 - 17 = 0.5 \, \text{m} \] \[ s - b = 17.5 - 10 = 7.5 \, \text{m} \] \[ s - c = 17.5 - 8 = 9.5 \, \text{m} \] Now substituting these values into Heron's formula: \[ A = \sqrt{17.5 \times 0.5 \times 7.5 \times 9.5} \] Calculating the product inside the square root: \[ 17.5 \times 0.5 = 8.75 \] \[ 8.75 \times 7.5 = 65.625 \] \[ 65.625 \times 9.5 = 623.4375 \] Now, taking the square root: \[ A = \sqrt{623.4375} \approx 24.98 \] Rounding to the nearest tenth, the area of the triangle is: \[ \boxed{25.0} \, \text{m}^2 \]