Find the area of a regular 12-gon inscribed in a circle with a radius of 8cm.

In order to find the area of ​​a regular dodecagon inscribed in a circle with a radius of 8 centimeters, you should recall the formula.
By this formula, we have.
S = (R²n × sin (360 °: n)): 2, where S is the area of ​​the corresponding polygon, R is the radius of the circumscribed circle, and n is the number of corners of this polygon.
Now let’s substitute the data specified in the task into the above-written formula and calculate the area of ​​the dodecagon.
S = (8² × 12 × sin (360 °: 12)): 2.
S = (64 × 12 × sin30 °): 2.
Recall that sin30 ° is 0.5.
S = 32 × 12 × 0.5.
S = 384 × 0.5.
S = 192 (cm²).
answer: S = 192 cm².