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A box of chocolates shaped like a regular hexagon is placed snugly inside of a rectangular box as shown in the figure.If the side length of the hexagon is 4 inches, what are the dimensions of the rectangular box? (30°-60°-90° )

Sagot :

MrRoyal

A regular hexagon has 6 congruent sides.

The dimension of the rectangle is 8 inches by [tex]4\sqrt 3[/tex] inches

How to determine the length of the rectangle

Start by calculating the value of x using the following cosine ratio

[tex]\cos(60) = \frac{x}{4}[/tex]

Make x the subject

[tex]x = 4 * \cos(60)[/tex]

Evaluate cos(60)

[tex]x = 4 * 0.5[/tex]

[tex]x = 2[/tex]

So, the dimension of the rectangle is:

[tex]Length = 2x + 4[/tex]

[tex]Width = 2x\sqrt 3[/tex]

This gives

[tex]Length = 2 * 2 + 4[/tex]

[tex]Length = 8[/tex]

[tex]Width = 2 * 2\sqrt 3[/tex]

[tex]Width = 4\sqrt 3[/tex]

Hence, the dimension of the rectangle is 8 by [tex]4\sqrt 3[/tex]

Read more about hexagons at:

https://brainly.com/question/2264170

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