Star in a Hexagon
Weekly Problem 20 - 2017
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?
Age
11 to 14
Challenge level
Problem
Image
The diagram shows a design formed by drawing six lines in a regular hexagon. The lines divide each edge of the hexagon into three equal parts.
What fraction of the hexagon is shaded?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: $\frac29$
Split each hexagon into 6 small triangles
Image
Image
Image
6$\times$6 + 6$\times$1 = 42 unshaded triangles
6$\times$1 + 1$\times$6 = 12 shaded triangles
Fraction shaded = $\dfrac{12}{42+12} = \dfrac{2}{7+2} =\dfrac29$