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What is the problem?
Assuming that the octagon is regular, what is the area of the shaded region
math student can you come look at my question and help me with it
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Apothem length 18.11
All youre given is the apothem? Do you know the side length?
Look at the case of the hexagon I drew above.
freebands - "Assuming that the octagon is regular, what is the area of the shaded region"
Ummm....WHAT "shaded region"??
Apparently there's a diagram that accompanies your question which you aren't sharing with us...
The side of the hexagon is the base of the upper triangle.
The apothem is the height of the triangle.
The area of the triangle is (1/2)bh = (1/2)sa
Since it's a hexagon, you have 6 triangles, so the area is 6 *(1/2)sa = 3sa
For an octagon, the area is 4sa (s = side, a = apothem)
In your case, the area of the entire octagon is 4(18.11 * 15.15)
How much of it is shaded?