Hello from MrBillDoesMath!
Answer:
320 sqrt(3)
Discussion:
Per the attachment,
cos(30 ) = n/ 32 => n = 32 cos(30) = 32 (sqrt(3)/2) = 16 sqrt(3)
So
area of shaded triangle =
area triangle DBC =
area triangle ADC - area triangle ABD =
1/2 (n) * (m + 40) - 1/2 n * m =
1/2 n*m + 1/2 (40n) - 1/2 n*m =
1/2(40n) =
20n =
20 ( 16 sqrt(3)) = as n = 16 sqrt(3)
320 sqrt(3)
Thank you,
MrB
