Area of a Hexagon: Find the Area with Radius r

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Homework Help Overview

The problem involves finding the area of a hexagon that has a circle of radius r inscribed within it. The original poster attempts to relate the area of the hexagon to the area of triangles formed within the hexagon.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relevance of the inscribed circle and whether it affects the area calculation. There are attempts to clarify the terminology used, particularly the difference between "impressed" and "inscribed." Some participants suggest using geometric properties of triangles to express the area in terms of the radius.

Discussion Status

There is ongoing clarification regarding the terminology and the nature of the problem. Some participants have provided insights into how to express the area of the hexagon using the radius, while others are exploring whether the problem fits within a calculus context.

Contextual Notes

Participants note that the problem may not require calculus and can be approached using basic geometric principles. There is a suggestion that the area should be expressed in terms of the radius of the inscribed circle.

Rossinole
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Homework Statement



A circle of radius r is impressed in a hexagon. Find the area of the hexagon.

Homework Equations



Area of a triangle = (1/2)bh

The Attempt at a Solution



The hexagon can be split up into six triangles, and with the formula for the area of a triangle, becomes (6)(1/2*bh).

Does the circle in the problem even matter? It makes it seem like there is more to the problem than there really is. Is there something I overlooked?
 
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what do you mean with : a circle of radius r is impressed in a hexagon? I think you have to use the radius of the circle on your answer. But if you could explain this part a lill bit more, what do you mean by that.
 
Do you mean "inscribed" instead of "impressed"? This question (post #1) is not really a Calculus problem; did you intend it to be for Calculus? Without using Calculus, this is a very simple exercise needing only intuitive knowledge of pattern in a shape and the pythagorean theorem.
 
It's just the sum of the areas of six identical triangles, each with two legs of length r and a central angle of 360 / 6 = 60 degrees. It's basic plane geometry.

- Warren
 
well, i think what they are asking you to do is express the area of the hexagon in terms of the radius of the circle. Your formula is right, just try to express the height of the triangles in terms of the radius, and use the letter r. Also notice that all three sides of the triangles are of size r.
 
It's meant to be a Calculus problem, or at least it's on my Calculus homework.

Alright, I went back and re-did this problem and got (3/2)r^2(sqrt(3)). I solved for the area of one equilateral triangle using r as one of the sides, multiplied it by six, and then reduced it to what is above.
 

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