In Fig. 4.178, 
(i) If DE = 4 cm, BC = 6 cm and area (
) = 16 cm2, find the area of 
.
(ii) If DE = 4 cm, BC = 8 cm and area (
) = 25 cm2, find the area of 
.
(iii) If DE : BC = 3 : 5. Calculate the ratio of the areas of 
and the trapezium BCED.
(i) We have , DE||BC, DE = 4cm, BC = 6cm and area (ΔADE) = 16cm2
In ΔADE and ΔABC
<A = <A (Common)
<ADE = <ABC (Corresponding angles)
Then, ΔADE ~ ΔABC (BY AA similarity)
So, By area of similar triangle theorem
Area of ΔADE/Area of ΔABC = DE2 /BC2
16/Area of ΔABC = 42/62
Or, Area (ΔABC) = 16 x 36/16
= 36cm2
(ii) We have , DE||BC, DE = 4cm, BC = 8cm and area (ΔADE) = 25cm2
In ΔADE and ΔABC
<A = <A (Common)
<ADE = <ABC (Corresponding angles)
Then, ΔADE ~ ΔABC (BY AA similarity)
So, By area of similar triangle theorem
Area of ΔADE/Area of ΔABC = DE2 /BC2
25/Area of ΔABC = 42/82
Or, Area (ΔABC) = 25 x 64/16
= 100 cm2
(iii) We have DE||BC, And DE/BC = 3/5 ……………(i)
In ΔADE and ΔABC
<A = <A (Common)
<ADE = <ABC (Corresponding angles)
Then, ΔADE ~ ΔABC (BY AA similarity)
So, By area of similar triangle theorem
Area of ΔADE/Area of ΔABC = DE2 /BC2
Area of ΔADE/Area of ΔADE + Area of trap. DECB = 32/52
Or, 25 area ΔADE = 9 Area of ΔADE +9 Area of trap. DECB
Or 25 area ΔADE - 9 Area of ΔADE = 9 Area of trap. DECB
Or, 16 area ΔADE = 9 Area of trap. DECB
Or, area ΔADE / Area of trap. DECB = 9/16