Welcome to polygon area calculation. Polygons are closed geometric shapes made up of straight line segments. Today we'll explore how to calculate the areas of different types of polygons, including triangles, squares, and more complex shapes like pentagons.
Let's start with the most basic polygon - the triangle. The area of any triangle can be calculated using the simple formula: Area equals one half times base times height. The base is any side of the triangle, and the height is the perpendicular distance from that base to the opposite vertex.
For rectangles and squares, the area calculations are straightforward. A rectangle's area equals length times width. A square is a special rectangle where all sides are equal, so its area is simply side length squared. These formulas work because we're essentially counting unit squares that fit inside the shape.
For regular polygons like hexagons, pentagons, and octagons, we use the apothem formula. The apothem is the distance from the center to the middle of any side, perpendicular to that side. The area equals one half times the perimeter times the apothem, or one half times n times side length times apothem.