In a regular hexagons ABCDEF prove that AB+Ac+AD+AE+AF=3AD
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Divide the hexagon into 4 triangles by joining AC, AD, AE .
Considering triangle ACD, v get AD= AC + CD
for Tri ADE , AD= AE + ED
Add the two eq=>
2AD= AC + CD + AE + ED
Now, AF = CD, because its a regular hexagon, therefore it has equal and parallel opposide sides.
Similarly , ED= AB
Substitute in the eq :
2AD= AB+ AC + AE + AF
Add one more AD both the sides and v get the desired result.
Divide the hexagon into 4 triangles by joining AC, AD, AE .
Considering triangle ACD, v get AD= AC + CD
for Tri ADE , AD= AE + ED
Add the two eq=>
2AD= AC + CD + AE + ED
Now, AF = CD, because its a regular hexagon, therefore it has equal and parallel opposide sides.
Similarly , ED= AB
Substitute in the eq :
2AD= AB+ AC + AE + AF
Add one more AD both the sides and v get the desired result.
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