Question 1062886
.
A regular decagon is inscribed inside a circle. The perimeter of the decagon is 50 units.

A: What is the approximate measure of the radius (rounded to the nearest hundredth of a unit)?

B: What is the approximate area of the circle (rounded to the nearest whole square unit)?

Select only one answer each for parts A and B.

	A: 8.09
	A: 2.63
	A: 7.69
	A: 4.25
	B: 22
	B: 186
	B: 206
	B: 57
~~~~~~~~~~~~~~~~~~~~


Let me show you how to estimate it without using calculator, computer, trigonometric tables and the Internet.
Using your (or my) BRAIN only !!!


<pre>
Since the perimeter is 50 units, the one side length is {{{50/10}}} = 5 units.


The central angle leaning one side is {{{360/10}}} = 36 degrees.

One half of this angle is 18 degrees: {{{alpha}}} = 18 degrees ~ {{{1/3}}} of the radian (approximately).

Hence, {{{tan(alpha)}}} =~ {{{1/3}}}, approximately.

Then the apothem, which is the height of the single central triangle, is about {{{(0.5*5)/((1/3))}}} = 2.5*3 = 7.5, approximately.

Then the area of one single central triangle is about {{{(1/2)*5*7.5}}} = 18.75.

Take it 10 times, and you will get the number 187.5 for the area.

Which number from the list is close to it?
</pre>

It is very useful if somebody will show you how to do it.


At least once in your life !!

-----------------------------------



OK, it looks like I made some mistake, comparing with the more accurate answer of the other tutor.


Nevertheless, my error of 10% is allowable for such a crude estimation.