Question

A trapezium with 3 equal sides and one side double the equal side, can be
divided into
equilateral triangles of
area.​

Answer 1

Step-by-step explanation:

Thus, triangle ADE and DEC are equilateral triangles having equal sides. Hence , the trapezium can be divided into 3 equilateral triangles of equal area.

Answer 2

Step-by-step explanation:

Let ABCD is a trapezium, in which

AD = DC = BC = a(say)

And AB = 2a

Draw medians through the vertices D and C on the side AB.

AE = EB = a

Now, in parallelogram ADCE, we have

AD = EC = a and AE = CD = a {opposite side in a parallelograms are equals}

In triangle ADE and DEC

AD = EC

AE = CD

DE = BC

BY SSS,

Thus, triangle ADE and DEC are equilateral triangles having equal sides.

Hence , the trapezium can be divided into 3 equilateral triangles of equal area.