Question

Triangle DEF (not shown) is similar to ABC shown, with angle B congruent to angle E and angle C congruent to angle F. The length of side DE is 6 cm. If the area of ABC is 5 square centimeters, what is the area of DEF ?

Answer 1

Area of ΔDEF is
`45\ cm^2`.

Explanation:

Given;

ΔABC and ΔDEF is similar and ∠B ≅ ∠E.

Length of AB =
`2\ cm` and

Length of DE =
`6\ cm`

Area of ΔABC =
`5\ cm^2`

Solution,

Since, ΔABC and ΔDEF is similar and ∠B ≅ ∠E.

Therefore,

`(Area\ of\ triangle\ 1)/(Area\ of\ triangle\ 2) =(AB^2)/(DE^2)`

Where triangle 1 and triangle 2 is ΔABC and ΔDEF respectively.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

`(5)/(Area\ of\ triangle\ 2) =(2^2)/(6^2)\\ (5)/(Area\ of\ triangle\ 2)=(4)/(36)\\ Area\ of\ triangle\ 2=(5*36)/(4) =5*9=45\ cm^2`

Thus the area of ΔDEF is
`45\ cm^2`.