Area of compound figures

Learning Objectives Identify simple geometric shapes within a compound figure. Decompose a compound figure into two or more non-overlapping rectangles or squares. Calculate the area of individual rectangular or square components of a compound figure. Apply the addition method to find the total area of a compound figure. Apply the subtraction method to find the area of compound figures with 'cut-outs'. Solve real-world problems involving the area of compound figures. Label the area of compound figures using appropriate square units. Ever wondered how much carpet you'd need for an L-shaped room or how much paint for a wall with a window? 🤔 In this lesson, you'll discover how to find the area of tricky, irregular shapes by breaking them down into simpler...

TermDefinitionExample AreaThe amount of surface a two-dimensional shape covers, measured in square units.A square with sides of 5 cm has an area of 25 square centimeters (25 cm²). Compound Figure (Composite Figure)A shape that is made up of two or more basic geometric shapes, such as rectangles and squares, joined together.An 'L'-shaped figure 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 shapes (like rectangles or squares) to make it easier to calculate its area.Cutting an 'L'-shaped figure with a line to create two separate rectangles. RectangleA four-sided flat shape with four straight sides and four right angles (90 degrees). Opposite sides are equa...

Area of a Rectangle $A = l \times w$ To find the area of a rectangle, multiply its length (l) by its width (w). Remember to use square units. 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. This is a special case of the rectangle formula. Area of Compound Figure (Addition Method) $A_{total} = A_{shape1} + A_{shape2} + ...$ When a compound figure is made of several simple shapes, find the area of each simple shape and then add them together to get the total area. Area of Compound Figure (Subtraction Method) $A_{total} = A_{larger\_shape} - A_{smaller\_shape}$ If a compound figure looks like a larger shape with a smaller shape 'cut out' of it, find the area of the larger shape...