Area of compound figures

Learning Objectives Decompose a compound figure on the coordinate plane into simpler polygons like triangles and rectangles. Calculate the lengths of horizontal, vertical, and diagonal sides of a polygon using coordinate differences and the distance formula. Calculate the area of a compound figure using the addition (decomposition) method. Calculate the area of a compound figure using the subtraction (bounding box) method. Apply the Shoelace Formula to find the area of any simple polygon given its vertices. Solve multi-step problems involving the area of composite shapes in a coordinate system. Ever wondered how a video game designer calculates the exact area of a complex kingdom on a map, or how an architect finds the square footage of an L-shaped room? 🗺️ Let's find o...

TermDefinitionExample Compound FigureA geometric figure that is formed by combining two or more simpler geometric shapes, such as rectangles, triangles, or trapezoids.An L-shaped polygon can be seen as two rectangles joined together, or one large rectangle with a smaller rectangle removed from a corner. VerticesThe corner points of a polygon. On the coordinate plane, each vertex is defined by an ordered pair (x, y).A triangle has three vertices, such as A(1, 2), B(5, 2), and C(3, 6). Decomposition MethodA strategy to find the area of a compound figure by breaking it down into smaller, non-overlapping, simple shapes. The total area is the sum of the areas of these smaller shapes.Splitting a plus-shaped figure into five squares and adding their individual areas together. Subtraction Method...

Distance Formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} Use this to find the length of any side of a polygon, especially diagonal ones, given the coordinates of its endpoints (x1, y1) and (x2, y2). This is essential for finding the base or height of triangles in the decomposition method. Area Formulas for Simple Shapes Rectangle: A = l \times w Triangle: A = \frac{1}{2} b \times h These are the building blocks for the Decomposition and Subtraction methods. After breaking down a compound figure, you apply these fundamental formulas to each simple shape. Shoelace Formula A = \frac{1}{2} |(x_1y_2 + x_2y_3 + ... + x_ny_1) - (y_1x_2 + y_2x_3 + ... + y_nx_1)| The most direct method for finding the area of a polygon with 'n' vertices. List the vertices (x, y) i...