What is the area of the shaded region below? Assume the hexagon is regular. Use your calculator and round your final answer to the nearest hundredth. (Picture included.)

Question

anonymous · Answer

attachment

mathstudent55 · Answer

What is the area of a regular polygon using the lengh of a side and the apothem?

anonymous · Answer

Oh, man if I knew. (No sarcasm intended.)

mathstudent55 · Answer

For a regular polygon,
Area = (apothem * perimeter) / 2
Multiply the apothem by the perimeter and divide by 2.
Can you find the area of the hexagon now?

anonymous · Answer

I think I can. Let me work out my answer.

mathstudent55 · Answer

Shaded area = area of hexagon - area of rectangle

mathstudent55 · Answer

For the hexagon, the side measures 22, so you can find the perimeter.
The apothem length is 19.05

anonymous · Answer

1257.3 - is what I got for the area of the hexagon.

mathstudent55 · Answer

Great.
Now you need the area of the rectangle.
A = L * W

anonymous · Answer

396 (?)

mathstudent55 · Answer

Correct.
Now subtract.

mathstudent55 · Answer

Shaded area = area of hexagon - area of rectangle

anonymous · Answer

1257.3 - 396 = 861.3 square units.

mathstudent55 · Answer

Correct

anonymous · Answer

And it's its square units right? I just wanna' make sure.

mathstudent55 · Answer

yes, an area is in square units