Answer: A) 52 square inches
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Explanation:
a = 8, b = 13, and c = 15 are the sides of the triangle
s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.
Those values are then plugged into Heron's Formula below
[tex]A = \sqrt{s*(s-a)*(s-b)*(s-c)}\\\\A = \sqrt{18*(18-8)*(18-13)*(18-15)}\\\\A = \sqrt{18*(10)*(5)*(3)}\\\\A = \sqrt{2700}\\\\A = \sqrt{900*3}\\\\A = \sqrt{900}*\sqrt{3}\\\\A = 30\sqrt{3}\\\\A \approx 51.9615\\\\A \approx 52\\\\[/tex]
The triangular plaque has an area of approximately 52 square inches.
