Area of compound figures

Learning Objectives Decompose a compound figure into simpler, non-overlapping geometric shapes. Select and apply the appropriate area formulas for various polygons and circles. Calculate the total area of a compound figure using both the addition and subtraction methods. Use the Pythagorean theorem or basic trigonometric ratios to determine missing side lengths required for area calculations. Calculate the area of composite figures that include sectors and segments of circles. Solve multi-step word problems involving the area of real-world compound figures. Ever planned to paint a room with an alcove or design a garden with a curved path? You were already thinking about the area of compound figures! 🏡 This tutorial will teach you how to find the area of complex shapes by b...

TermDefinitionExample Compound FigureA two-dimensional shape made by combining two or more basic geometric shapes (e.g., rectangles, triangles, circles). It is also known as a composite figure.An L-shaped polygon can be seen as two rectangles joined together. A window shape could be a rectangle combined with a semicircle on top. DecompositionThe strategic process of breaking a compound figure into simpler, non-overlapping shapes whose area formulas are known.Splitting an L-shaped figure into two distinct rectangles by drawing a single horizontal or vertical line. Addition MethodA technique for finding the total area of a compound figure by calculating the area of each decomposed shape and then adding them together.For an ice-cream cone shape, you would find the area of the triangle and th...

Area Addition Principle A_{total} = A_{1} + A_{2} + ... + A_{n} Use this when the compound figure is formed by joining shapes together. Decompose the figure, find the area of each individual part (A_1, A_2, etc.), and sum them to get the total area. Area Subtraction Principle A_{shaded} = A_{larger} - A_{smaller} Use this for figures with cutouts or holes. Identify the larger, encompassing shape and the smaller, removed shape. Calculate both areas and subtract the smaller from the larger. Area of a Sector (Degrees) A_{sector} = (\frac{\theta}{360}) \times \pi r^2 Use this to find the area of a pie-slice portion of a circle, where 'r' is the radius and 'θ' (theta) is the central angle of the sector in degrees.