anonymous
  • anonymous
How would I solve this question? All of the triangles in the figure below are congruent. What is the area of the figure? Note that all measurements are in centimeters. Note that the apothem shown is equal to 2 (sqrt)3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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KingGeorge
  • KingGeorge
A nice easy trick to this problem, is to notice that the area of the equilateral triangles is the same as the area of the hexagon. So you just have to find one to find the total area. The area of the hexagon is \[A={1 \over 2}ap\]where a is the apothem and p is the perimeter. We know the apothem to be \(2\sqrt3\) and the perimeter to be \(6\cdot4=24\) So the area of the hexagon is\[{1 \over 2}48\sqrt3 ={24\sqrt3}\]Therefore, the total area is\[2\cdot(24\sqrt3)=48\sqrt3\]
KingGeorge
  • KingGeorge
Wait, is the height of the triangle 3? Was I misreading the diagram?

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anonymous
  • anonymous
But, that's not an answer. D: However, 24 (sqrt)3 ^2 is. WOuld that be it?
anonymous
  • anonymous
The height of the triangle is 3. Yes.
KingGeorge
  • KingGeorge
If the height of the triangle is 3, then the area of each triangle is \[{1\over2}\cdot3\cdot4=6\]So then the answer should be \[24\sqrt3+6\cdot6=24\sqrt3+36\]
KingGeorge
  • KingGeorge
There are 6 triangles, so that's why I multiplied the 6 by 6.
anonymous
  • anonymous
That is a possible answer. :D
anonymous
  • anonymous
Is that answer squared?
KingGeorge
  • KingGeorge
No. That's the entire answer. \[24\sqrt3+36 \;\;\;\text{cm}^2\]
anonymous
  • anonymous
Oh, sweet. :D Thanks man!
KingGeorge
  • KingGeorge
You're welcome.

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