Can Someone Solve this Geometry Word Prob???

Question

an equilateral triangle and regular hexagon (all sides are of equal length) have equal perimeters. what is the ratio of their areas?

Answer 1

Perimeter of the triangle and hexagon is 6x

Area of triangle (made up of side lengths 2x on all three sides)
= 1/2 base times height
= 1/2.2x.SQRT(36x^2-9x^2)
= x.SQRT(27x^2)
= x.3x.SQRT(3)
= 3x^2SQRT(3)

Area of hexagon (made up of side lengths x on all six sides)
= 6(1/2 base times height of a little triangle side length x)
= 6. 1/2 . x . SQRT(x^2 - x^2/4)
= 6. 1/2 . x . SQRT(3x^2 /4)
= 6. 1/2 . x . x/2 SQRT(3)
= (3/2) x^2 SQRT(3)

Triangle is twice as big as the hexagon

Answer 2

Triangles have 3 sides
Hexagons have 6 sides
A regular side length would be 1
Heagons are more complicated than triangles so for this reason we give the hexagon side length 1. This means it has a perimeter of 6 (6 sides x length 1).
From this we know our triangle has perimeter 6, which means it has 3 sides of 2 (3 sides of length 2 = perimeter of 6)
Hexagons can be broken down into 6 equilateral triangles.
Equilateral triangles can be broken down into 4 equilateral triangles. ( see previous source for clear diagram, but ignore their working)
As each triangle has 3 sides length 1 all of the triangles in the hexagon and big triangle are equal in size. This means the area for the ratio is 4:6, or 2:3

Answer 3

For ratio problems you can actually pick numbers that comply with the ratio. Let's use 36 as the perimeter just because both 3 and 6 divide into it. So the triangle has a side of 12 and the hexagon 6.

triangle's area = (sqrt3 / 4) side^2 = 36*sqrt 3

The regular hexagon is made up of 6 equilateral triangles, so hexagon's area = 6*(sqrt3 / 4) side^2 = 54* sqrt 3

So ratio is 36:54 = 2:3

Not too many right answers on here, so be selective!!

Answer 4

Let the perimeter be P.
So, length of a side of triangle= P/3
Length of a side of hexagon= P/6

Ratio of their Areas = (P/3 : P/6)^2

=(3 : 6)^2
=(1 : 2)^2
= 1:4

Answer 5

Let the sides be H and T. Solve each figure for the area Ah and At in terms of a side. In the case of the triangle, it's easy; with the hexagon, you will have to add up pieces. The perimeters are, of course, 6H and 3T; equate these and do the obvious simplifications.

Answer 6

The ratio of the sides is (p/3)/(p/6) =2
so the ratio of the area of the triangle to the hegagone is 4

Answer 7

thats easy
the area of tha triangle is 4 times bigger than the exagon
if the trainlges sides are 8, then its perimeter would be 24
in order for the haxagons perimeter to be 24 teh sides would ahve to be 4 each
the are of the triangle would be 64
and teh area of tha hexagon would be 16

16:64 = 1:4

and im 13 years odl and never had geometry before and i could solve this.??

Answer 8

You would need to know the side lengths

Answer 9

wouldn't that just be 3:5?

Answer 10

You can find the answer here along with how they got their answer. Hope it helps!

http://mathcentral.uregina.ca/QQ/database/QQ.02.06/trevor1.html