Question

In the given figure, ABCDE is a pentagon. EG // DA meets BA produced at G and CF // DB meets AB produced at F. The ratio of area of pentagon ABCDE : area of $\Delta GDF$ is

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

Answer 1

The correct option is D

1 : 1

(i) EG // DA ..... (given)

(ii) area $\Delta AED$ = area $\Delta AGD$ ..... (triangles on the same base and between the same parallels)

(iii) CF // DB ..... (given)

(iv) area $\Delta BDC$ = area $\Delta BFD$ …. (triangles on the same base and between the same parallels)

(v) adding equations (ii) and (iv) and adding area $\Delta ABD$ to both sides we get

area $\Delta AED$ + area $\Delta ABC$ + area $\Delta BDC$ = area $\Delta AGD$ + area $\Delta ABC$ + area $\Delta BFD$

area of pentagon ABCDE = area of $\Delta GDF$

Thus, area of pentagon ABCDE : area of $\Delta GDF$ is 1 : 1

Hence (D)