Find the area of the following triangle. Round your answers to the nearest tenth. a=4.8in,b=6.3in,c=7.5in Use the paperclip button below to attach files.

To find the area of a triangle when all three sides are known, we can use Heron's formula. Heron's formula states that if a triangle has sides of lengths \(a\), \(b\), and \(c\), then the area \(A\) of the triangle is given by:<br /><br />\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]<br /><br />where \(s\) is the semi-perimeter of the triangle, calculated as:<br /><br />\[ s = \frac{a + b + c}{2} \]<br /><br />Given:<br />\(a = 4.8 \, \text{in}\)<br />\(b = 6.3 \, \text{in}\)<br />\(c = 7.5 \, \text{in}\)<br /><br />First, calculate the semi-perimeter \(s\):<br /><br />\[ s = \frac{4.8 + 6.3 + 7.5}{2} = \frac{18.6}{2} = 9.3 \, \text{in} \]<br /><br />Next, use Heron's formula to find the area:<br /><br />\[ A = \sqrt{9.3(9.3 - 4.8)(9.3 - 6.3)(9.3 - 7.5)} \]<br />\[ A = \sqrt{9.3 \times 4.5 \times 3 \times 1.8} \]<br />\[ A = \sqrt{9.3 \times 4.5 \times 3 \times 1.8} \]<br />\[ A = \sqrt{116.946} \]<br />\[ A \approx 10.8 \, \text{in}^2 \]<br /><br />Therefore, the area of the triangle is approximately \(10.8 \, \text{in}^2\).