To find the area of the triangle, we can use Heron's formula, which states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c)/2
In this case, the side lengths of the triangle are given as 17.5 yd, 42 yd, and 45.5 yd. We can use these values to calculate the semiperimeter:
s = (17.5 yd + 42 yd + 45.5 yd)/2 = 52 yd
Now we can use Heron's formula to find the area:
Area = sqrt(52 yd(52 yd - 17.5 yd)(52 yd - 42 yd)(52 yd - 45.5 yd))
Area = sqrt(52 yd * 34.5 yd * 10.5 yd * 6.5 yd)
Area = sqrt(120022.5) yd²
Area ≈ 346.3 yd²
Therefore, the area of the triangle is approximately 346.3 yd².