Question

Points A, D, and C are collinear. Find the area of ΔADB. Show your work. If the answer is not an integer, give the exact answer in simplest radical form.

Answer 1

PLZ HElp

Answer 2

area triangle ADB equal area triangle ACB minus area triangle DCB

yes ?

sin 45 = CB / 6

sqrt2 / 2 = CB /6

6sqrt2 /2 = CB

3sqrt2 = CB

sin 30 = CB / AB

1/2 = 3sqrt2 / AB

AB = 2*3sqrt2

AB = 6sqrt2

AC^2 = AB^2 -CB^2

AC^2 = 72 -18

AC^2 = 54

AC = sqrt54

AC = 3sqrt6

area triangle ACB = CB *AC /2

area triangle ACB = (3sqrt2 *3sqrt6) / 2

area triangle ACB = (9sqrt12)/2

area triangle ACB = (18sqrt3)/2

area triangle ACB = 9sqrt3

length DC = length CB = 3sqrt2

area triangle DCB = BC *DC /2

area triangle DCB = (3sqrt2 *3sqrt2) /2

area triangle DCB = 9*2/2

area triangle DCB = 9

area triangle ADB = area triangle ACB - area triangle DCB

area triangle ADB = 9sqrt3 - 9

hope helped