A box of chocolates shaped like a regular hexagon is placed snugly inside of a rectangular box as shown in the figure.If the sid

Question

3 years ago

12

e length of the hexagon is 4 inches, what are the dimensions of the rectangular box? (30°-60°-90° )

1 answer:

OLEGan [10] · Answer 1 · 2022-11-30T03:34:21+03:00

A regular hexagon has 6 congruent sides.

The dimension of the rectangle is 8 inches by $4\sqrt 3$ inches

<h3>How to determine the length of the rectangle</h3>

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

$\cos(60) = \frac{x}{4}$

Make x the subject

$x = 4 * \cos(60)$

Evaluate cos(60)

$x = 4 * 0.5$

$x = 2$

So, the dimension of the rectangle is:

$Length = 2x + 4$

$Width = 2x\sqrt 3$

This gives

$Length = 2 * 2 + 4$

$Length = 8$

$Width = 2 * 2\sqrt 3$

$Width = 4\sqrt 3$

Hence, the dimension of the rectangle is 8 by $4\sqrt 3$