A box is being designed to contain 4 stacks of chocolate wafers. Each chocolate wafer is in the shape of a regular hexagon of side length 3 cm. What is the area of the rectangular base of the box? Give your answer as k√3 where k is irrational

1 Answer
Oct 20, 2017

Answer:

#k=315/4#

Explanation:

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The measure of each interior angle #x# of a regular polygon is given by : #x=((n-2)*180)/n#, where n is the number of sides.
So in a regular hexagon,
interior angle #x=((6-2)*180)/6=120^@#
Fig 1 shows a regular hexagon with side #s#,
#BM=MC=s*sin60=(sqrt3s)/2#
#AM=s*cos60=s/2#
As shown in Fig 2, #EFGH# is the rectangular base of the box,
given that side length of the regular hexagon #s=3# cm,
#=> EF=2s+3*s*cos60=2xx3+3xx3xx1/2=21/2# cm
#=> EH=5*s*sin60=5xx3xxsqrt3/2=(15sqrt3)/2# cm
Given area of the rectangular base #=ksqrt3#,
#=> ksqrt3=21/2*(15sqrt3)/2=(315sqrt3)/4 " cm"^2#
#=> k=315/4#,
As #k# can be expressed as #p/q#, where #p and q# are integers and #q!=0#, #k# is rational.