Question

The area of the spiderweb is approximately
.
A)
A spider weaved a web in the shape of a regular nonagon. What is the area of the web, to thenearest hundredth, if each side measures 5.4 millimeters?
(1 point)
mm

Answer 1

Area = (n s^2) / (4 tan(π/n)) for a regular n-gon.

Here n = 9, s = 5.4 mm:
Area = (9·5.4^2) / (4·tan(π/9))
= (9·29.16) / (4·tan(20°))
≈ 262.44 / 1.455880937
≈ 180.26 mm^2

So the area ≈ 180.26 mm^2 (to the nearest hundredth).