Question 1007115: A regular hexagon is cut from a square of side 6 inches, a.) what is the
apothem of the hexagon? B.) what is the area of the hexagon? Answer by Edwin McCravy(20055) (Show Source):
You can put this solution on YOUR website! A regular hexagon is cut from a square of side 6 inches, a.) what is
the apothem of the hexagon? B.) what is the area of the hexagon?
The red line below is the apothem.
In the figure
AB is given 6 inches. It is divided into 4 parts,
AD = DC = CE = EB = 6/4 = 3/2 inches.
Triangle DOE is equilateral, so DO = DE = DC+CE = 3/2+3/2 = 3 in.
Using the Pythagorean theorem on right triangle DOC,
DOē = DCē + OCē
3ē = (3/2)ē + OCē
9 = 9/4 + OCē
9-9/4 = OCē
36/4-9/4 = OCē
27/4 = OCē
= OC
= OC
= OC
= OC = the length of the apothem in inches.
For the area of the hexagon, first we find the area of the
equilateral triangle DOE:
inē
And as we see below, the hexagon is made up of 6 congruent equilateral
triangles all congruent to DOE, its area is 6 times the area of triangle
DOE.
So the area of the hexagon is or inē.
Edwin
