Answer:

4:1

Step-by-step explanation:

Given:△ABC and △BDE are equilateral.

BD=

2

1

BC as D is the midpoint of BC

Since △ABC and △BDE are equilateral.

Their sides would be in the same ratio

BE

AB

=

ED

AC

=

BD

BC

Hence by SSS similarity,△ABC∼△BDE

And, we know that the ratio of area of triangle is equal to the ratio of the square of corresponding sides.

So,

areaof△BDE

areaof△ABC

=

BD

2

BC

2

=

(

2

BC

)

2

BC

2

since BD=

2

BC

=

BC

2

4BC

2

=

1

4

Hence

areaof△BDE

areaof△ABC

=

1

4

=4:1