Assume all the variables are nonnegative.
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
If G is the midpoint of CD, and AC is parallel to DB, then AC = DH.
Therefore, G is the midpoint of AH and ΔACE is similar to ΔDBE.
As AC : DB = 1 : 3
⇒ Area of ΔACE : Area of ΔDBE = 1² : 3² = 1 : 9
We are told that Area ΔACE = Area ΔAEG.
⇒ Area ΔACG = 2 × Area ΔACE
As AC = DH, and G is the midpoint of CD:
⇒ ΔACG ≅ ΔHDG
⇒ Area ΔHDG = 2 × Area ΔACE
Area of quadrilateral EGHB = Area of ΔDBE - Area ΔHDG
= Area of ΔDBE - 2 × Area of ΔACE
Therefore:
Using the ratio of Area ΔACE : Area ΔDBE = 1 : 9