Fill in the blanks to make the correct statement.

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

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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.


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