Note that area in question = area of △UYZ + area of trapezoid UYXW
m∠VUW + m∠WUY = 90°
m∠ZUY + m∠WUY = 90°
So
m∠VUW = m∠ZUY
By ASA congruence, △UVW is congruent to △UYZ.
area of △UVW + area of trapezoid UYXW = area of square UVXY = 5 * 5 = 25 sq units
Since △UVW is congruent to △UYZ,
area of △UYZ + area of trapezoid UYXW = area of △UVW + area of trapezoid UYXW = 25 sq units
(Also, I made this to help me figure it out because I was very lost on this problem for awhile! You can see that as the value of a changes, the area in question stays the same, at 25 sq units.)
https://web2.0calc.com/img/upload/9dc0601484f88e63c19f0354/ugh3.jpg
Pretend that we just got all the people that liked the movie in a room together. The question is what is the probability that a randomly selected person in that room is aged 18-34 ?
probability = number of people aged 18-34 in the room / number of people in the room
probability = num of people aged 18-34 that liked the movie / num of people that liked the movie
probability = 12 / (12 + 5 + 9)
probability = 12 / 26
probability ≈ 0.46