Question

Question 40

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

Answer 1

3, equal.

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
$\therefore$ AE = EB = a
Now, in parallelogram ADCE, we have
AD = EC = a and AE = CD = a [$\because$ opposite sides in a parallelogram are equal]
In $\Delta ADE$ and $\Delta DEC$,
AD = EC
AE = CD
and DE = DE [common]
By SSS, $\Delta ADE=\Delta DEC$
By triangle rule, $\Delta ADE\cong \Delta DEC$
Thus, $\Delta ADE$ and $\Delta DEC$ are equilateral triangles having equal sides
Similarly, in parallelogram DEBC, we can show that $\Delta DEC\cong \Delta ECB$
Hence, the trapezium can be divided into 3 equilateral triangles of equal area.