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Can someone please help me with this?

Can someone please help me with this?-example-1

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Answer:


403.06 cm^2; 100.77cm^2

Explanation:

Ok, step 1. What's the measure of the internal angle of a dodecagon? After some splitting in triangles you get that's
(n-2)\pi = 10\pi. That makes each angle measure
(10)/(12)\pi.

That allows us to split the whole figure in 12 isosceles triangles with (congruent) angles of
\frac5{12}\pi. Consider just one, red in my picture. The height of that triangle - orange "vertical" line - can be found with some trigonometry as
3tan \frac5{12}\pi \approx 11.2 cm

At this point one triangle has area
\frac12 \cdot 6\cdot 11.2 = 33.6 cm^2 and the whole cookie has area as 12 triangles
403.06 cm^2.

After her eating spree, you're left with 3 triangles, for a grand total of
100.77 cm^2

Can someone please help me with this?-example-1
User Dienekes
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