For the polygon $A B C D E F$ if $A F + E D = B C$ and $A B = E F + D C$ , then it's perimeter is .

8 a

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6 a

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10 a

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Solution

The correct option is A $8 a$
We know perimeter is the sum of all the side lengths of any closed figure.
For the polygon, we have to find out the lengths of $E D$ and $C D$ .
Now, $A F + E D = B C$
$\Rightarrow E D = 2 a - a = a$
Similarly, $A B = E F + C D$
$\Rightarrow C D = 2 a - a = a$ units.
Now, that we know the lengths of all the sides.
The perimeter of $A B C D E F$
$= A B + B C + C D + D E + E F + F A$
$= 2 a + 2 a + a + a + a + a$
$= 8 a$

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