# In the figure DE || BC. If DE = 4 cm, BC = 8 cm and area (ΔADE) = 25 sq. cm, find the area of ΔABC. Given: DE || BC

DE = 4cm, BC = 8cm and area ( ADE) =25 sq. cm

In ABC and ADE

B = D [ DE || BC and AB is transversal,

Corresponding angles are equal]

C = E [ DE || BC and AC is transversal,

Corresponding angles are equal]

BAC =DAE [common angle] ABC ~ ADE [by AAA similarity]

Now, we know that, the ratio of two similar triangles is equal to the square of the ratio of their corresponding sides.  [given]  ar( ABC) = 25×4

ar ( ABC) = 100cm2

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