Answer:
CD = 12
BD = 9
area = 150
Explanation:
BD/CD = CD/AD = BC/AC
BD/CD = CD/16 = 15/AC
BC/CD = AC/AD = (AD + BD)/AC
15/CD = AC/16 = (16 + BD)/AC
BC/BD = AC/CD = (AD + BD)/BC
15/BD = AC/CD = (16 + BD)/15
15/BD = (16 + BD)/15
225 = 16BD + BD²
BD² + 16BD - 225 = 0
(BD - 9)(BD - 25) = 0
BD = 9
(CD)² = 16BD
CD = 4√BD
CD = 4√9
CD = 12
area = bh/2
area = (AD + BD)(CD)/2
area = (16 + 9)(12)/2
area = 150