2 Answers

Zett · Answer 1 · 2023-11-16T20:53:56+0000

Given:

A regular heptagon with 7 sides is inscribed in a circle.

The radius is 10 mm.

The inscribed angle in the regular heptagon is 51.43 degrees.

Consider,

$\begin{gathered} a^2=10^2+10^2-2(10)(10)\cos 51.43^(\circ) \\ a^2=200-200(0.6235) \\ a=8.68 \end{gathered}$

The area of the heptagon is,

$\begin{gathered} A=(7)/(4)a^2\cot ((180^(\circ))/(7)) \\ =(7)/(4)(8.68)^2\cot ((180^(\circ))/(7)) \\ =273.7\operatorname{mm} \end{gathered}$

Answer: option a) 273.641 mm² ( approximately)

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