The area of triangle AQRS is approximately 939.32 square inches.
To find the area of triangle AQRS using Heron's formula, we can first calculate the semi-perimeter (s) of the triangle.
The semi-perimeter is found by adding the lengths of all three sides of the triangle and dividing by 2.
In this case, the semi-perimeter (s) is (85 + 23 + 94)/2 = 101 inches.
Next, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c and semi-perimeter s is given by:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
Using the given side lengths, we substitute the values into the formula:
Area = sqrt(101 * (101 - 85) * (101 - 23) * (101 - 94))
Area = sqrt(101 * 16 * 78 * 7)
Area ≈ 939.32 inches²