Question

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

Answer 1

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

Explanation:

Let ABCD be a trapezium, in which

AD = DC = BC = a  ...(say)

And AB = 2a  ...[Given]

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 parallelogram are equal]

In ΔADE and ΔDEC,

AD = EC

AE = CD

And DE = DE  ...[Common]

BY SSS, ΔADE = ΔDEC

By triangle rule, ΔADE ≅ ΔDEC

Thus, ΔADE and ΔDEC are equilateral triangles having equal sides.

Similarly, in parallelogram DEBC, we can show that ΔDEC ≅ ΔECB.

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