Problem: In the figure, it is given that angle C=90∘, AD=DB,DE⊥AB,AB=20, and AC=12. The area of quadrilateral ADEC is:
Answer Choices:
A. 75
B. 5821
C. 48
D. 3721
E. (none of these)
Solution:
Since AB=20 and AC=12,BC=16. Since △BDE∼△BCA, Area △BCA Area △BDE=162102. But Area △BCA=21⋅12⋅16=96.
∴ Area △BDE=3721
and the required area is 96−3721=5821.
