# 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

<A = <A (Common)

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

<A = <A (Common)

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)

<A = <A (Common)

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

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