Question

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

Answer 1

`k=315/4`

Explanation:

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.