## Austin_Rain Group Title 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 2 years ago 2 years ago

1. Austin_Rain Group Title

2. KingGeorge Group Title

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$2\cdot(24\sqrt3)=48\sqrt3$

3. KingGeorge Group Title

Wait, is the height of the triangle 3? Was I misreading the diagram?

4. Austin_Rain Group Title

But, that's not an answer. D: However, 24 (sqrt)3 ^2 is. WOuld that be it?

5. Austin_Rain Group Title

The height of the triangle is 3. Yes.

6. KingGeorge Group Title

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 $24\sqrt3+6\cdot6=24\sqrt3+36$

7. KingGeorge Group Title

There are 6 triangles, so that's why I multiplied the 6 by 6.

8. Austin_Rain Group Title

That is a possible answer. :D

9. Austin_Rain Group Title

10. KingGeorge Group Title

No. That's the entire answer. $24\sqrt3+36 \;\;\;\text{cm}^2$

11. Austin_Rain Group Title

Oh, sweet. :D Thanks man!

12. KingGeorge Group Title

You're welcome.