Area of the shaded triangle?
A hard-level "Area" problem.A regular hexagon is "six equilateral triangles". That one sentence turns almost every hexagon area problem into a ratio problem.
GivenThe regular hexagon has area 72 cm². Alternate vertices are joined
Hints
- A regular hexagon splits into six identical equilateral triangles when you draw six lines from the centre. Start there.
- The hexagon is 72 cm², so each small triangle is 72 ÷ 6 = 12 cm².
- Now look at just one side of the shaded triangle. It passes exactly through the midpoint of the line from the centre to a vertex.
- That means this side cuts each of the two neighbouring triangles exactly in half — blue inside the shaded triangle, orange outside, and the two are equal.
- The same thing happens in all six. Exactly half of every small triangle lies inside the shaded one. The three orange corners that stick out add up to exactly what is left inside.
- So the shaded triangle is exactly half the hexagon. 72 ÷ 2 is the answer.
Answer 36cm²
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?