Answer:
The fraction is 1/4
Step-by-step explanation:
we know that
The area of an equilateral triangle, using the law of sines is equal to
where
x is the length side of the triangle
In this problem
Let
b ----> the length side of the regular hexagon
2b ---> the length side of the equilateral triangle
step 1
Find the area of the six triangles
Multiply the area of one triangle by 6
we have
substitute
step 2
Find the area of the regular hexagon
Remember that, a regular hexagon can be divided into 6 equilateral triangles
so
The area of the regular hexagon is the same that the area of 6 equilateral triangles
we have
substitute
step 3
To find out what fraction of the total area of the six triangles is the area of the hexagon, divide the area of the hexagon by the total area of the six triangles