Question

O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth if necessary.

Answer 1

Given the figure of a dodecagon

As shown the height = h = 17

The area of the dodecagon is as follows:

$A=6\times h\times s$

A = the area of the dodecagon, s = the length of its side

The relation between the side length (s) and the height (h) is as follows:

$s=2h\cdot\tan 15$

So, the area will be:

$A=6\cdot h\cdot(2h\cdot\tan 15)$

Substitute with h = 17

$A=6\cdot17\cdot(2\cdot17\tan 15)^{}=929.2478$

Rounding to the nearest tenth

so, the answer will be Area = 929.2