Calculating the areas of polygons with a smartphone light sensor

This study explores finding the areas of polygons with a smartphone light sensor. A square and an irregular pentagon were chosen as our polygons. During the activity, the LED light was placed at the vertices of our polygons, and the illuminance values of this LED light were detected by the smartphone light sensor. The smartphone was placed on a rotating time-lapse device, and this device was placed at the intersection point of the line segments in the polygons. These line segments were also connected to the vertices of these polygons; therefore, the square was composed of four triangles and the pentagon of five triangles. While the rotating time-lapse device was rotating around itself, it captured the maximum illuminance values of the LED light. Using these maximum illuminance values, we calculated the lengths of the line segments. In addition, we knew the period of the rotating time-lapse device and the duration elapsed between two consecutive maximum illuminance values. Thus, we could calculate the angle between two consecutive line segments. With these values, we could also calculate the areas of the triangles in the polygons. Then, the areas of these triangles were summed to obtain the areas of the square and pentagon.