Question

A composite figure is comprise of a semicircle, a hexagon, and a rectangle.
How can you decompose the composite figure to determine its area?

as a circle, two trapezoids, and a rectangle
as a semicircle, a pentagon, and two triangles
as a semicircle, a hexagon, and a rectangle
as a circle, six triangles, and a rectangle

Answer 1

Choose: as a semicircle, a hexagon, and a rectangle.

Reason: the figure is already made of those three pieces, so to find the total area you add the areas of the three parts:
- Area = Area(semicircle) + Area(hexagon) + Area(rectangle).

Formulas you may need:
- Semicircle: (1/2)πr² (r = radius).
- Rectangle: length × width.
- Regular hexagon: (3√3/2) s² (s = side length). (Equivalently a regular hexagon = 6 equilateral triangles, each with area (√3/4) s².)

The other choices are incorrect descriptions of the given composite figure (for example choice 4 uses a full circle instead of a semicircle).