Question
Autumn wants to calculate the area of the regular hexagon below using rectangles and triangles. What is the minimum number of shapes she could use?
A regular hexagon
Two triangles and one rectangle
Two rectangles and one triangle
Two triangles and two rectangles
Six triangles and no rectangles
A regular hexagon
Two triangles and one rectangle
Two rectangles and one triangle
Two triangles and two rectangles
Six triangles and no rectangles
Answers
GPT-4o mini
To calculate the area of a regular hexagon effectively using basic shapes, we can consider the following approaches:
1. **Two triangles and one rectangle**: This option could potentially work if the rectangles can fit neatly within the hexagon and the triangles can cover the remaining areas. However, this arrangement may become complicated.
2. **Two rectangles and one triangle**: This approach is also plausible but may require more shapes than necessary.
3. **Two triangles and two rectangles**: This option likely offers flexibility but again may utilize more shapes than needed.
4. **Six triangles and no rectangles**: A regular hexagon can be divided into 6 equilateral triangles. Since the hexagon has 6 sides, it's straightforward to visualize dividing it directly into 6 equal triangles, where each triangle fits perfectly without needing any other shapes.
Considering all the options, the minimum number of shapes that can effectively cover the area of a regular hexagon without leaving any gaps is:
**Six triangles and no rectangles.**
This makes the fourth option the most efficient one. Therefore, the minimum number of shapes Autumn could use is **6 triangles**.
1. **Two triangles and one rectangle**: This option could potentially work if the rectangles can fit neatly within the hexagon and the triangles can cover the remaining areas. However, this arrangement may become complicated.
2. **Two rectangles and one triangle**: This approach is also plausible but may require more shapes than necessary.
3. **Two triangles and two rectangles**: This option likely offers flexibility but again may utilize more shapes than needed.
4. **Six triangles and no rectangles**: A regular hexagon can be divided into 6 equilateral triangles. Since the hexagon has 6 sides, it's straightforward to visualize dividing it directly into 6 equal triangles, where each triangle fits perfectly without needing any other shapes.
Considering all the options, the minimum number of shapes that can effectively cover the area of a regular hexagon without leaving any gaps is:
**Six triangles and no rectangles.**
This makes the fourth option the most efficient one. Therefore, the minimum number of shapes Autumn could use is **6 triangles**.