Question

Can someone show me the steps to solve the problem?

Answer 1

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