Question

The perimeter of the regular hexagon with its center at H is 48 and its apothem is . Which is the area of the shaded region?

Answer 1

What is Apothem?

Answer 2

The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides.

Answer 3

but you have not given the apothem in the question?

Answer 4

what is the length of apothem?

Answer 5

its 6 square root 3

Sorry it didnt paste into the question.

Answer 6

ok
so we have
area = (½)(apothem)(perimeter)

and you can find the area of that triangle and subtract both to get the area of the shaded region right?

Answer 7

area of triangle=1/2*base*height....height here is apothem

Answer 8

umm ok

Answer 9

if you get stuck just post where u r stuck here itself.. i believe u will be fine :D

Answer 10

so its 8 times apothem and i get the area of the triangle?

Then i subtract the area of the shaded region by that?

Answer 11

i didnt get you? what is 8 times the apothem??

Answer 12

uhh whats 6 square root 3?

Answer 13

6 square root 3 is the apothem right?

Answer 14

yes

Answer 15

yes so for the area of the hexagon we have area = 1/2*perimeter*apothem...
perimeter is 48 apothem is 6 root 3 so u get that...

now for area of triangle we have

1/2*base/height

base=perimeter/6
height=apothem=6 root 3

subtract both the areas :D