Problem 7 · 2021 Math Kangaroo
Medium
Geometry & Measurement
area-decomposition
Six congruent rhombuses, each of area 5 cm², form a star. The tips of the star are joined to draw a regular hexagon, as shown. What is the area of the hexagon?
Show answer
Answer: C — 45 cm²
Show hints
Hint 1 of 2
Each rhombus splits into two small equilateral triangles, so one such triangle has area 2.5.
Still stuck? Show hint 2 →
Hint 2 of 2
The hexagon is the six-rhombus star plus six more of those same triangles in the gaps.
Show solution
Approach: count equal small triangles
- The six rhombuses give the star an area of 6×5 = 30.
- Each rhombus is two equal equilateral triangles, so each small triangle has area 2.5.
- Filling the hexagon adds six more identical triangles: 6×2.5 = 15.
- Hexagon area = 30 + 15 = 45 cm², choice (C).
Mark:
· log in to save