Question

In the figure, EF $\parallel$ AB and E is the mid-point of FG. Find the ratio of area (ABCDO) to the sum of area (BAFGO) and area (AEB).

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 3

Answer 1

The correct option is B

1 : 2

In the figure, draw a line parallel to AB and EF passing through O. We can clearly see that $△$ABF and $△$ABC are having the same base and are between the same parallels.

So, Area ($△$ABF) = Area ($△$ABC) --------------------------------------I

Similarly, Area ($△$ABE) = Area ($△$ABC) ------------------------------II

Similarly, we have $△$OGC and $△$ODC. Given that E is the mid-point of FG,

Area ($△$OGF) = 2 × Area ($△$ODC) -------------------------------------III

Area (ABCDO) = Area ($△$ABC) + Area ($△$ODC)

Area (BAFGO) + Area ($△$AEB) = Area ($△$ABF) + Area ($△$OGF) + Area ($△$AEB)

From I, II and III, we can write

Area (BAFGO) + Area ($△$AEB) = 2 × (Area ($△$ABC) + Area ($△$ODC))

So, the ratio = [Area ($△$ABC) + Area ($△$ODC)]/[2 × (Area ($△$ABC) + Area ($△$ODC))] = 1/2 = 1 : 2