Question

$	riangle ABC$ and $	riangle XYZ$ are equilateral triangles of 54 cm sides. All smaller triangles like $	riangle ANM$, $	riangle OCP$, $	riangle QPX$ etc. are also equilateral triangles. Find the area of the shape MNOPQRM.

Accepted Answer

B. The sides of $	riangle ABC$ are trisected by the intersecting equilateral triangle $	riangle XYZ$. Thus each side of the hexagon MNOPQRM is $54 / 3 = 18$ cm. The area of a regular hexagon of side $s = 18$ cm is: $$	ext{Area} = \frac{3\sqrt{3}}{2} \cdot s^2 = \frac{3\sqrt{3}}{2} \cdot 18^2 = \frac{3\sqrt{3}}{2} \cdot 324 = 486\sqrt{3} 	ext{ sq. cm.}$$

Geometry: Hexagon Area from Equilateral Triangles

Explanation

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