(Q7) ∆ABC ∼ ∆DEF. BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm2. Determine the area of ∆DEF.

ABCDEF3 cm4 cm54 cm2

Solution:

Given : ∆ABC ∼ ∆DEF

BC = 3 cm

EF = 4 cm

∆ABC = 54 cm2

∴ ∆ABC ∼ ∆DEF, we have

∆ABC
∆DEF
=
BC2
EF2

[∵ The ratio of two similar triangles is equal to the ratio of the squares of the corresponding sides].

=
∴ ∆DEF =
×
= cm2