Final answer:
To find the area of the regular hexagon, Lin decomposed it into six identical triangles, while Andre decomposed it into a rectangle and two triangles.
Step-by-step explanation:
To find the area of the regular hexagon, we can use Lin's method of decomposing it into six identical triangles. The formula to find the area of a triangle is A = 1/2 * base * height. Since the hexagon has 6-inch sides, the base of each triangle would be 6 inches, and the height can be found using the Pythagorean theorem. The height (h) is equal to the square root of the side length squared minus half of the side length squared (h = √(6^2 - (6/2)^2)). Once we have the height, we can calculate the area of one triangle and multiply it by 6 to get the total area of the hexagon.
Andre decomposed the hexagon into a rectangle and two triangles. The rectangle has a length equal to the side length of the hexagon (6 inches) and a width equal to the height of the triangle. The area of the rectangle is length times width. The two triangles have the same base as the rectangle (6 inches) and a height equal to the side length of the hexagon. The area of each triangle is 1/2 times the base times the height. To find the total area, we add the areas of the rectangle and the two triangles.