Question
Question: 
Now, we need to find the ratio of the area of quadrilateral ABDE to the area of ΔCDF.
To find this let us draw the figure and shade the area which we need to find.
Here, the shaded regions are quadrilateral ABDE and ΔCDF.
From the figure we get that –
Area of Quadrilateral ABDE = Area of ΔACE − Area of ΔBCD
By substituting the value of ΔACE from equation (1) we get –
Area of ABDE =x−ΔBCD …………………….. (2)
We can also observe that –
Area of ΔCDF=Area of ΔBCF− Area of ΔBCD.
By substituting the value of ΔACE from equation (1) we get –
Area of ΔCDF=x−ΔBCD ……………………….. (3)
Now, we will find the ration of ar ABDE: ar ΔCDF
Therefore,
Area if ΔCDFArea of Quadrilateral ABDE
By substituting the values from equation (1) and (2) , we get that –
⇒x−ΔBCDx−ΔBCD
By cancelling the common factors from numerator and denominator, we get –
⇒11
Therefore, the ration of ar ABDE: ar ΔCDF is 1:1
Hence, option A. is the correct answer.
Note: Students should know that, if all the sides of two triangles are proportional, then this is called SSS similarity and the two triangles called congruent or similar triangles.
For example: In our question –
For ΔACE&ΔBCF
BCAE=CFCE=BFAC
By substituting their values, we get –
66=77=88
By cancelling the common factors from numerator and denominator, we get –
1=1=1
Therefore, it proves that ΔACE≅ΔBCF which is congruent.