Question

For the polygon $ABCDEF$ if $AF+ED=BC$ and $AB=EF+DC$, then it's perimeter is .

• A. $8a$
• B. $6a$
• C. $10a$

Answer 1

The correct option is A $8a$

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 $ED$ and $CD$.
Now, $AF+ED=BC$
$\Rightarrow ED=2a-a=a$
Similarly, $AB=EF+CD$
$\Rightarrow CD=2a-a=a$ units.
Now, that we know the lengths of all the sides.
The perimeter of $ABCDEF$
$=AB+BC+CD+DE+EF+FA$
$=2a+2a+a+a+a+a$
$=8a$