Find the area of a 6-gon with side length 12? Round to a whole number.

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Answer 1 · 2018-04-10T19:33:45

374

Area of regular hexagon= $(3sqrt3)/2a^2$ where $a$ is side length

Answer 2 · 2018-04-10T20:19:23

This is approximately $374.12 " units"^2$ to 2 decimal places

Rounded this gives $374" units"^2$

Objective is to find the area of $1/2$ the triangle then multiply that by 12 to obtain the total area.

Area of a triangle is $1/2xx"base"xx"hight"$
Tony B

The angle marked in blue is $(360^o)/6 = 60^o$
Consider just $1/2$ of the triangle:

Tony B

The sum of angles in a triangle is $180^o$

Angle ABC is $90^o$ so angle BCA is $180^o-90^o-30 = 60^o$

Length AB can be determined from $tan(60^0)=(AB)/(BC)$

$tan(60^o)=(AB)/6$

The height $AB=6tan(60)$

But $tan(60) = sqrt(3)" "$ as an exact value.

So height $AB=6tan(60)=6sqrt(3)$

Thus area of $DeltaABC = a= 1/2xx"base"xx"height"$

$color(white)("dddddddddddddddddd")a= 1/2xx color(white)("d")6 color(white)("d")xx color(white)("d")6sqrt(3) color(white)("ddd")=18sqrt(3)$

We have 12 of these in the 6-gon so the total area is:

Area of the whole $A=12xx18sqrt(3) = 216sqrt(3)$

This is approximately $374.12 " units"^2$ to 2 decimal places
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Note that $216sqrt(3) = 3/2sqrt(3)xx12^2$

Matching the $3/2sqrt(3)color(white)(.)a^2$ given by Briana M

color(white)(.)