If ΔABC ∼ Δ DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm², then the area of the triangle DEF is :

125 cm²

Concept Used

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

⇒ \(\frac{Area\; of \; triangle\; ΔABC}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{BC}{EF}\))²

⇒ \(\frac{80}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{4}{5}\))²

⇒ \(\frac{80}{Area\; of \; triangle\; ΔDEF}\) = (\(\frac{16}{25}\))

⇒ Area of ΔDEF = \(\frac{80 \;×\; 25}{16}\) = 125 cm²

Therefore area of ΔDEF is 125 cm².