Area and Perimeter of 2D Shapes Purpose: find perimeter of simple and complex shapes; find area of simple and complex shapes; find missing lengths given area or perimeter; find area or distances in order to solve problems about density or amount per unit *note: Complex shapes are those which combine two or more simple shapes by putting them together and/or subtracting smaller shapes from a larger one. Definitions Perimeter (P): the distance (one-dimensional) around the outside edges of a shape Area (A): the space (two-dimensional) inside a shape Circumference (C): the distance around a circle Radius (r): the distance from the center of a circle to its outside edge (half the diameter) Diameter (d): the distance all the way across a circle through its middle (twice the radius) Parallelogram: a quadrilateral with opposite sides parallel and congruent and opposite angles congruent (includes “slanted rectangles,” rectangles, rhombi, and squares) Kite: a quadrilateral with opposite angles congruent and two different pairs of adjacent congruent sides Rhombus: a quadrilateral with opposite angles congruent and all sides congruent Trapezoid: a quadrilateral with at least one pair of opposite sides parallel Base (b): a side of a shape that may be viewed as its bottom Height (h): the distance moving perpendicular from the base to the top of a shape Regular polygon: a shape with all straight edges whose internal angles are all congruent and all sides are congruent Apothem (a): the distance from the center of a regular polygon to the midpoint of any of its sides (must be perpendicular to sides); the height of any triangle that can be formed within a regular polygon whose base is one of the polygon’s sides and tip is the polygon’s center Units: the unit of measurement used to specify a distance (1D and includes perimeter, lengths, etc.) or area (2D) Ex: in., cm, mm, m, ft, yd, mi., etc. Formulas *note: maKe sure all values used when applying any formula are given in terms of the same units before doing any calculations (this may require doing conversions) Perimeter: sum of all sides Perimeter of regular polygons: P=s*n, where s is the length of one side and n is the number of sides Circumference: C= πd n Length of the arc of a sector of a circle: C = πd × , 360 where n is the number of degrees of the sector’s angle € € bh A = Area of a triangle: 2 Area of a parallelogram: A = bh € h(b + b ) A = 1 2 Area of a trapezoid: 2 € pq A = Area of a kite or rhombus: 2 , where p is one diagonal and q is the other€ aP A = Area of a regular polygon: € 2 2 Area of a circle: A = πr € n A = πr2 × Area of a sector of a circle: 360 , where n is the number of degrees of the sector’s angle € *remember: Complex € shapes require you to find multiple distances or areas and combine them as appropriate. *MaKe sure you include the appropriate units with your final answer (square units for area, units for perimeter). .