Help idk how to do this ASAP please

The area of ∆DEF = 4.5in²

Step-by-step explanation:

From the above diagram,

∆BAC ~∆DEF

It is important to note that if two triangles are similar, the ratio of their areas is equal or equivalent to the ratio of the areas of their sides

This means for the above question, that

We have the bigger triangle = ∆BAC has a side of 4 in and Area = 8 in²

The small triangle has a side of 3in

Finding the scale factor k = ratio of the sides of both Triangles

k = 4/3

k² = (4/3)²

k² = 16/9

Hence,

Area of ∆BAC/ Area of ∆DEF = 16/9

8in²/Area of ∆DEF = 16/9

We cross Multiply

8 in² × 9 = Area of ∆DEF × 16

Divide both sides by 16

Area of ∆DEF = 72/16

= 4.5in²

Therefore, the Area of ∆DEF rounded to the nearest tenth = 4.5in²