Area of compound figures

Learning Objectives Define and identify compound figures. Decompose compound figures into basic geometric shapes (rectangles, squares, and triangles). Apply appropriate area formulas to calculate the area of each decomposed basic shape. Sum the areas of the individual basic shapes to find the total area of a compound figure. Solve real-world problems involving the area of compound figures. Accurately label area measurements with correct square units. Ever wondered how much carpet you'd need for a room with an L-shape, or how much paint for a wall with a triangular top? 🤔 It's not just one simple rectangle! In this lesson, you'll learn how to find the total area of complex shapes by breaking them down into simpler, familiar ones like rectangles and triangles....

TermDefinitionExample Compound FigureA geometric figure that is made up of two or more basic geometric shapes, such as rectangles, squares, or triangles, joined together.An L-shaped room is a compound figure because it can be split into two rectangles. DecompositionThe process of breaking down a complex compound figure into simpler, non-overlapping basic geometric shapes.Splitting an L-shaped figure into two separate rectangles to make it easier to calculate its area. AreaThe amount of two-dimensional space a shape or surface covers, measured in square units.If a square has sides of 2 cm, its area is 4 square centimeters (4 cm²). RectangleA four-sided polygon with four right angles, where opposite sides are equal in length.A standard door or a piece of paper is typically a rectangle. Squa...

Area of a Rectangle $A = l \times w$ To find the area of a rectangle, multiply its length ($l$) by its width ($w$). This rule is fundamental for decomposing many compound figures. Area of a Square $A = s \times s$ or $A = s^2$ To find the area of a square, multiply the length of one side ($s$) by itself. Since all sides are equal, it's a special case of the rectangle formula. Area of a Triangle $A = \frac{1}{2} \times b \times h$ To find the area of a triangle, multiply half of its base ($b$) by its height ($h$). The height must be perpendicular to the base. Area of a Compound Figure (Addition Method) $A_{total} = A_1 + A_2 + ... + A_n$ To find the total area of a compound figure, decompose it into $n$ basic shapes, calculate the area of each individual...