Question

The area of a regular hexagon is 38 cm^2. What is the area of a regular hexagon with sides eight times as long?

Answer 1

area of a regular hexagon = \[\frac{ side^23\sqrt{3} }{ 2 }\]
38=side^2 3root/2
76=side^2 3root3
76=side^2root27
14.6262=side^2
side=3.82 so one side is 3.82 cm. now 3.82 times 8=? then just plug the known info back into the formula to solve. BTW my answer is rounded, so better if you do it yourself.

Answer 2

You might also see that because these figures have to be similar (they are both regular hexagons), there exists a ratio of their areas consistent with their ratio of side lengths 1:8.

An area unit is just a length unit squared (A = k l^2), so the ratio between the areas is 1^2 : 8^2 or 1:64.

Answer 3

Thanks you guys !

Answer 4

You're welcome. :)