Question

​In the adjoining figure ABCD is a parallelogram of perimeter 21. It is subdivided into smaller parallelograms by drawing lines parallel to the sides. The numbers shown are the respective perimeters of the parallelograms in which they are marked. (For example the perimeter of the parallelogram LMNP is 11). Find the perimeter of the shaded parallelogram.

Answer 1

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Here is your answer.

Perimeter of parallelogram ABCD is 21

Perimeter of Smaller parallelogram are 11 , 8 , 5, and 4

Hence Sum of Perimeter of all the smaller parallelogram are = 11 + 8 + 5 + 4
= 28

Perimeter of Shaded portion parallelogram= Perimeter of all the smaller parallelogram - Perimeter of Parallelogram ABCD
$= 28 - 21 \\ = 7$
Therefore Perimeter of the Shaded portion parallelogram is 7.

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Answer 2

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Here is the answer.

Perimeter of large parallelogram ABCD is 21

Perimeter of small parallelogram are 11, 8, 5, 4

Sum of Perimeter of all the smaller parallelogram are

= 11 + 8 + 5 + 4

= 28

Perimeter of parallelogram of shaded portion = Perimeter of all smaller parallelogram - Perimeter of bigger parallelogram ABCD

$= 28 - 21 \\ \\ = 7$
Hence, The perimeter of parallelogram of shaded portion is 7.

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