Question

BAC is similar to EDF. if the area of BAC equals 8 in.² what is the area of EDF? Plz help

Answer 1

Area of ΔEDF = 4.5 in²

Explanation:

In the figure attached,

ΔBAC ~ ΔEDF

Property of similarity,

" If two triangles are similar then their corresponding angles will measure the same."

Scale factor for ΔBAC to ΔEDF =
`\frac{\text{Side EF}}{\text{Side BC}}`

=
`(3)/(4)`

"Ratio of the area of similar triangles = Square of the ratio of their corresponding sides"

`\frac{\text{Area of triangle FDE}}{\text{Area of triangle CAB}}` =
`((3)/(4))^2`

`\frac{\text{Area of triangle FDE}}{8}=(9)/(16)`

Area of ΔEDF =
`(9* 8)/(16)`

= 4.5 square inches

Therefore, area of ΔEDF = 4.5 in²