Area of Composite Figures

Geometry · Axiom Academy

LESSON Area of Composite Figures Finding area by breaking shapes apart or combining them. 1. Two Strategies for Any Composite Figure To find the area of a composite figure, you reshape the problem into ones you can already solve. Watch the L-shape below split along a dividing line into two plain rectangles — once it's in familiar pieces, the area is just bookkeeping. Break the figure into parts, find each area, then add them together. Start with a larger shape, then subtract the "missing" pieces or holes. Divide the figure into separate, non-overlapping pieces, find each area, and sum them. Take this L-shaped room : a dashed line splits it into rectangle A and rectangle B . 3. Worked Example — Adding Strategy Find the area of this composite figure: a rectangle with a triangle sitting on top (think of a house outline). 4. Method 2 — Subtract the Areas When a figure has a piece removed — a hole, a cut-out, a notch — find the area of the whole outer shape, then subtract what's missing. Watch the inner rectangle get punched out. 5. Worked Example — Subtracting Strategy A square garden (12 ft × 12 ft) has a circular fountain (radius 3 ft) in the center. Find the area of the garden excluding the fountain. (Use .) 6. Worked Example — Finding Missing Dimensions Sometimes a side isn't labeled and you have to work it out first. Find the shaded area of this L-shape, where two inner lengths are marked with a "?". A reliable routine for any composite-figure problem:

This is the written version of the interactive lesson above. See the full Geometry course.