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Polygons(n>3)

In a regular ...

Question

In a regular hexagon $A B C D E F$ , $A B = a, B C = b$ and $C D = c$ . Then, $A E$ is equal to

a + b + c

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2 a + b + c

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b + c

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a + 2 b + c

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Solution

The correct option is C $b + c$
We have
$A B = a, B C = b$ and $C D = c$
$∴$ $A C = a + b$
In $△ A C D$ , we have
$A C + C D = A D$
$\Rightarrow$ $a + b + c = A D$
In $△ A E D$ , we have
$A D + D E = A E$
$\Rightarrow$ $a + b + c - a = A E$ $[∵ D E = B A = - a]$
$\Rightarrow$ $A E = b + c$

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