The area of a regular hexagon is 1500 square centimeters. What is its perimeter?

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Answer 1 · 2016-01-04T17:01:33

$=144.18 cm$

The formula for area of a hexagon is

area $color(blue)(=(3sqrt3)/2 xx (side) ^2$

The area given $=color(blue)(1500 cm^2$ , equating the same

$(3sqrt3)/2 xx (side) ^2= 1500$

$(side) ^2= 1500 xx 2/(3sqrt3)$

(note : $sqrt3=1.732$ )

$(side) ^2= 1500 xx 2/(3xx1.732)$

$1500 xx 2/(5.196)$

$= 3000/(5.196)$

$= 577.37$

side $= sqrt577.37$

the side $= 24.03cm$

Perimeter of the hexagon (six sided figure) = $6 xx side$

Perimeter of the hexagon = $6 xx 24.03$

$=144.18 cm$