help please i got first part of question i am stuck on second part see attached

Question

anonymous · Answer

attachment

anonymous · Answer

found height as 8.7sqrt3

anonymous · Answer

@ranga or @e.mccormick

anonymous · Answer

i know as well area for trapezoid is 1/2h(b1+b2)

anonymous · Answer

@hartnn

anonymous · Answer

answer in book is 
A=489.7cm^2

anonymous · Answer

AI=17.4cos 60=17.4*1/2=8.7
AD=8.7+31.8=40.5
area=(40.5+24.5)/2*8.7sqrt3

anonymous · Answer

i am in just geometry now so i dont know sin or cos yet

hartnn · Answer

ok, so you can find AI using pythagoras theorem

hartnn · Answer

you have h = 8.7 sqrt 3
b1 = 24.5
you need b2 = 31.8 + AI

anonymous · Answer

How you calculated h ?

anonymous · Answer

sqrt3/2*17.4 = h

hartnn · Answer

good, you used the fact that side opposite to 60 degree angle is sqrt 3 /2 times the hypotenuse

to find AI, you can use the fact that side opposite ti 30 degree angle is half the hypotenuse

anonymous · Answer

?? so 8.7 sqrt 3/2?

anonymous · Answer

oh i get it so 17.4/2 :)

hartnn · Answer

but hypotenuse is 17.4
so AI = 17.4/2 
yes! :)

anonymous · Answer

so now add 8.7 to the 31.8 to get 40.5 then i got it and plug into the 1/2h(b1+b2) :D

hartnn · Answer

you got it :D

anonymous · Answer

thanks geometry is new to me - still trying to understand it all kinda trippy lol

hartnn · Answer

with some practice, you'll love geometry :)