regarding traingle

Note that when a triangle is cut by a line parallel to the base , then the smaller triangle and the bigger triangle are similar( use AA  similarity for this)

 Now,

 suppose ABC is cut by a line DE parallel to BC.

So,  triangle ABC and  triangle ADE are the similar triangles.

We know that the ratio of areas of similar triangles is equal to the ratio of the square of  their corresponding sides.

According to question,

area (ADE) is the same as  area (BCED)

So, this tells us that

area (ABC)=are(ADE)+area(BCED)=2 area(ADE).

SO, are( ABC)=2 area (ADE)