Question

The given figure shows a pentagon ABCDE, EG, drawn parallel to DA, meets BA produced at G and CF drawn parallel to DB, meets AB produced at F. The area of $\Delta GDF$ is equal to area of ______ .

• A. $\Delta ABD$
• B. Quadrilateral GBDE
• C. Pentagon ABCDE
• D. Quadrilateral AFCD

Answer 1

The correct option is C Pentagon ABCDE

(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 $\Delta BFD$

$\Rightarrow$Area of pentagon ABCDE = area of $\Delta GDF$ (From the figure)