Heptagon's 83628

Calculate a regular heptagon's perimeter if its shortest diagonal length is u=14.5cm.

Correct answer:

o =  56.3283 cm

Step-by-step explanation:

n=7 u=14.5 cm  α=nn−2​⋅ 180=77−2​⋅ 180=7900​≐128.5714 ∘  u2 = a2+a2 − 2⋅ a⋅ a⋅ cos α u2 =2a2 − 2⋅ a2⋅ cos α u2/2 =a2(1 − cos α)  a=1−cosαu2/2​​=1−cos128.57142857143° u2/2​​=1−cos128.57142857143° 14.52/2​​=1−(−0.62349)14.52/2​​=8.04689 cm  o=n⋅ a=7⋅ 8.0469=56.3283 cm

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