36.2k views
5 votes
hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

User Dan Mason
by
7.8k points

2 Answers

7 votes

Perimter\ of\ equilateral\ triangle\ =36\\ a- \ side\ of\ triangle\\ 36=3a\ |:3\\ a=12\\\\ Area\ of\ equilateral\ triangle:\\ A=(a^2√(3))/(4)\\ A=(12^2√(3))/(4)\\ A=(144√(3))/(4)=36\sqrt3 \\\\ Hegagon\ can\ be\ divided\ into\ 6\ equilateral\ small\ triangles.\\Area\ of\ one\ of\ them: A_s=(A)/(6)=(36\sqrt3)/(6)=6√(3)\\ s-side\ of\ equilateral\ =\ side\ of\ small\ triangle\\ A_s=(s^2√(3))/(4)=6√(3)\ |*4 \\ s^2\sqrt3=24\sqrt3\ |\sqrt3\\ s^2=24\\ s=√(24)
√(24)=√(4*6)=2\sqrt6\\\\ Side\ of\ hexagon\ equals\ 2\sqrt6\ inches
User Adam Weitzman
by
7.9k points
6 votes

Answer:


2√(6)

Explanation:

Perimeter of equilateral triangle = 36 inches

Formula of perimeter of equilateral triangle =
3* side


36=3* side


(36)/(3) = side


12= side

Thus each side of equilateral triangle is 12 inches

Formula of area of equilateral triangle =
(√(3))/(4) a^(2)

Where a is the side .

So, area of the given equilateral triangle =
(√(3))/(4) * 12^(2)

=
36√(3)

Since hexagon can be divided into six small equilateral triangle .

So, area of each small equilateral triangle =
(36√(3))/(6)

=
6√(3)

So, The area of small equilateral triangle :


(√(3))/(4)a^(2) =6√(3)

Where a is the side of hexagon .


(1)/(4)a^(2) =6


a^(2) =6* 4


a^(2) =24


a =√(24)


a =2√(6)

Hence the length of a side of the regular hexagon is
2√(6)

User Shubham Patel
by
7.8k points

No related questions found