Question

the length of perimeter of a regular decagon which surrounds a circle of radius 12cm ​

Answer 1

The length of perimeter of a regular decagon is "158.4 cm".

Step-by-step explanation:

Let side of regular decagon = x

To, find the length of perimeter of a regular decagon = ?

$x^{2} =12^{2} +12^{2} -2\times 12 \times 12 \cos36$

⇒ $x^{2} =144 +144 -288 \times \cos36$

⇒ $x^{2} =288 -288 \times -0.1279$

⇒ $x^{2} =288 -36.84$

⇒ $x^{2} =288 -36.84=251.16$

⇒ x = 15.84 c

∴ The length of perimeter of a regular decagon = 10 × 15.84 =158.4 cm

Hence, the length of perimeter of a regular decagon is 158.4 cm.