Assuming that the octagon is regular, what is the area of the shaded region below? Use your calculator and round your final answer to the nearest hundredth.

Question

anonymous · Answer

attachment

anonymous · Answer

@jim_thompson5910 A little help please? >.< Sorry to bug you~

jim_thompson5910 · Answer

I'm sure you know the area of the square right?

anonymous · Answer

Yeah, 
A = L x W
A = 11 x 11
A = 121

jim_thompson5910 · Answer

ok what is the area of the octagon

jim_thompson5910 · Answer

hint: the apothem will be used

austinl · Answer

$$A=\frac{1}{2} \times n \times s \times r$$
n= number of sides
s= length of side
r= apothem

anonymous · Answer

292.16 is what I got.

jim_thompson5910 · Answer

austinL has the right formula

austinl · Answer

Unfortunately, that is not the same answer that I got.

anonymous · Answer

If his formula is correct, the answer should be 584.32 square units.

austinl · Answer

But that is including the area of the square that you do not need.

jim_thompson5910 · Answer

it is correct formula for the area of the polygon

think about it like this: break the octagon into 8 triangles

|dw:1372813369235:dw|

jim_thompson5910 · Answer

each triangle is congruent and each triangle looks like this

|dw:1372813444716:dw|

jim_thompson5910 · Answer

so the area of this triangle is (1/2)*r*s

there are n of these triangles, so multiply this by n to get (1/2)*n*r*s

anonymous · Answer

849.92 is what I have now then.

jim_thompson5910 · Answer

Area of Shaded Region = (Area of Octagon) - (Area of Square)

austinl · Answer

$$A_{shaded region}=A_{octagon} - A_{rectangle}$$
$$A_{shaded region}=(\frac{1}{2} \times n \times s \times r) - (l \times w)$$

anonymous · Answer

607.92 is what I have now. >.<

jim_thompson5910 · Answer

what did you get for the area of the octagon?

anonymous · Answer

88.

jim_thompson5910 · Answer

that's not correct

jim_thompson5910 · Answer

use the formula given above