Finding Area of Composite Figure

Pre-Algebra · Axiom Academy

EXAMPLE Finding the Area of a Composite Figure Break an L-shaped figure into two rectangles, then decompose it a second way to check the answer. An L-shaped room has the dimensions shown below. Find its total floor area. Then split the figure a different way to confirm the result. The L-shaped figure, drawn to its stated measurements. Nice work! You found the area of an L-shaped figure two different ways and got the same answer both times. Decompose first: a composite figure breaks into simple rectangles whose areas you already know how to find. Area of a rectangle: , then add the pieces together. More than one path: a horizontal cut ( 84 + 48 ) and a vertical cut ( 96 + 36 ) both give . Built-in check: decomposing a second way is a quick way to verify your total. The same break-it-into-pieces strategy handles far more than L-shapes — any region you can cut into rectangles, triangles, or other basic shapes is fair game.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.