Directions:

Question:
In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC?

Option A):
9
Option B):
4.5
Option C):
13.5
Option D):
18

Correct Answer is Option B):
4.5

Explanation:
If we take AE as the base of triangle AEC, then the height is CD.
The height of the triangle is therefore, 9 (given).
To find the base we need to see that triangles AEB and CDE are similar. The ratio AB: CD, is therefore equal to the ratio AE: ED. The given information shows that the ratio is 3:9, or 1:3. Now dividing AD (4) in this ratio gives us AE as 1.
The area of AEC =  base x height
=1/2 x 9 = 4.5