SOLUTION: This ornate box is in the shape of a regular hexagon. The length of each edge is nine and a half centimetres. The distance across the box from the middle of one edge to the middle

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Question 1117862: This ornate box is in the shape of a regular hexagon. The length of each edge is nine and a half centimetres. The distance across the box from the middle of one edge to the middle of the opposite edge is 17cm. What is the area (to two decimal places) of the base of the box in square centimetres?

Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
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Make a drawing as is described. Do you find a special 30-60-90 triangle with a couple of side lengths you can identify?




* According to the description, you should identify these quantities for one of the special 30-60-90 triangles:
leg 8%261%2F2
short leg 4%263%2F4
hypotenuse, same as an edge of the hexagon 9%261%2F2.

If the description is reliable, then area for ONE of these special triangles is %281%2F2%29%284%263%2F4%29%288%261%2F2%29; but the hexagon contains twelve of these, so the hexagon area is:
6%284%263%2F4%29%288%261%2F2%29.
Compute this how you want.


* Does the description really work?
8.5%5E2%2B4.75%5E2+=+9.5%5E2
72.25%2B22.5625=90.25
94.8125=90.25FALSE;
94.8125%3C%3E90.25
The given description does not work.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given information is self-contradictory. If the hexagon is regular with sides of length 9.5cm, then the distance across the box is not 17cm; it is 9.5*sqrt(3) cm, or about 16.45cm.

Given the difference between those two measurements, it will not be possible to calculate the area of the base correct to 2 decimal places using the given value of 17cm.

In fact the area of a regular hexagon with side length s (calculated as the area of 6 equilateral triangles with side length s) is

6%2A%28%28s%5E2%2Asqrt%283%29%29%2F4%29

For a side length of 9.5cm, the area is, to 2 decimal places, 234.48 cm^2.