Answer:
Step-by-step explanation:
You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...
sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)
-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)
Of course, you know that ...
sin(π/4) = cos(π/4) = (√2)/2
cos(π/3) = 1/2
sin(π/3) = (√3)/2
So, the desired value is ...
sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)
Comparing this form to the desired answer form, we see ...
A = 2
B = 3
Area = 1/2 base x height so you would find the area of one of the 3 larger sides which would be 12.2x6.1=74.42 then divide it by 2 which is 37.21. Then multiply it by 3 because of the other sides that are the same which gets you 111.63. Then you find the area of the bottom triangle by doing 5.3x6.1= 32.33 then divide it by 2 which is 16.165. Then you add both numbers together and you get 127.795. Answer is 127.795
