Final answer:
To find the probability of a point landing in the red-shaded triangle, we compare the area of the triangle to the total area of the square. Using Heron's formula, we calculate the area of the triangle by plugging in the side lengths. The probability is then found by dividing the area of the triangle by the area of the square.
Step-by-step explanation:
To find the probability of a randomly selected point landing in the red-shaded triangle, we need to compare the area of the red triangle to the total area of the square. In this case, the area of the red triangle can be found using Heron's formula, since we know the lengths of its sides. The formula is:
A = sqrt(s(s-a)(s-b)(s-c))
Where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter of the triangle (s = (a+b+c)/2).
In this case, a = 11, b = 22, and c = 22. Plugging these values into the formula, we get:
A = sqrt((55)(33)(33)(22))
Next, we need to find the area of the square. Since the length of one side of the square is 22, the area of the square is 22^2 = 484.
Finally, we can find the probability by dividing the area of the red triangle by the area of the square:
P = A/484 = sqrt((55)(33)(33)(22))/484