Area of rectangles and squares

Learning Objectives Calculate the area of rectangles and squares when dimensions are expressed as algebraic expressions. Solve for unknown dimensions of a rectangle or square given its area and one other dimension, potentially involving solving linear or quadratic equations. Calculate the area of a rectangle or square defined by vertices on a Cartesian plane. Apply area formulas to solve multi-step word problems, including those involving unit conversions or composite shapes. Use the Pythagorean theorem to find a missing dimension of a rectangle given its diagonal and one side, and then calculate its area. Formulate a simple proof related to the area of rectangles or squares. How does a GPS calculate the area of a rectangular park from satellite data? 🛰️ It all comes down to...

TermDefinitionExample AreaThe measure of the two-dimensional space enclosed by a shape. It is always expressed in square units (e.g., cm², m², square units).A floor tile that is 1 foot by 1 foot has an area of 1 square foot. RectangleA quadrilateral with four right angles (90°). Opposite sides are equal in length and parallel.A standard sheet of A4 paper, a smartphone screen, or a door. SquareA special type of rectangle where all four sides are equal in length. It also has four right angles.A single square on a chessboard or a standard wall tile. DimensionsThe measurements that define the size of a shape. For a rectangle, these are its length and width. For a square, it is the side length.A rectangle might have dimensions of 5 meters by 3 meters. Cartesian PlaneA two-dimensional coordinat...

Area of a Rectangle A = l \times w The area (A) of a rectangle is found by multiplying its length (l) by its width (w). Ensure both dimensions are in the same unit before multiplying. Area of a Square A = s^2 The area (A) of a square is found by squaring its side length (s). This is a special case of the rectangle formula where l = w = s. Pythagorean Theorem (for finding dimensions) l^2 + w^2 = d^2 In a rectangle, the length (l), width (w), and diagonal (d) form a right-angled triangle. This theorem can be used to find a missing side length if the other side and the diagonal are known.