Question -
Answer -
Given: (1)ΔABC is equilateral triangle.
(2) ΔBDE is equilateral triangle.
(3) D is the midpoint of BC.
To find: 
PROOF : Let us draw the figure as per theinstruction given in the question.
We know that area of equilateral triangle = 
, where a is the side of the triangle.
Let us assume that length of BC is a cm.
This means that length of BD is 
cm, Since D is the midpointof BC.
------(1)
------(2)
Now, ar(ÄABC) : ar(ÄBDE) = 
(from 1 and 2)
=
Hence we get the result ar(ÄABC) : ar(ÄBDE) =