Area of a hexagon

Geometry Level 1

Two congruent equilateral triangles, each with an area equal of $36~cm^2$ , are placed on top of each other so that they form a regular hexagonal overlap. Find the area of the hexagon.

32~cm^2

20~cm^2

30~cm^2

24~cm^2

2 solutions

Jonathan Quarrie
Oct 4, 2017

Reducing the image down to a single triangle, and presenting it as 9 congruent triangles. We can see that the hexagon is made of 6 of the 9 triangles.

$\dfrac{36}{9} \cdot 6 = \large\boxed{24}$

Edwin Gray
Mar 3, 2019

The area of an equilateral triangle is (s^2) sqrt(3)/4. The side of a hexagon is s/3. The area of a hexagon with side s/3 = 6 [(1/2) (s^2/9) sqrt(3)/2 = (s^2) sqrt(s)/6. So the hexagon is 2/3 the area of the triangle, and(2/3) 36 = 24.

Area of a hexagon

2 solutions

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