Area of composite figures worksheet for Pre-Algebra
In Pre-Algebra composite figures are built from rectangles, triangles and circles, and the sheets ask for perimeter as well as area. For area, break the shape into pieces you know and add them, or subtract a piece that has been cut out; for perimeter, add only the edges around the outside.
Also taught in Geometry, at its own level and with its own examples.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
A 10 by 6 rectangle with a 4 by 3 rectangle cut out of one corner
Whole rectangle: 10 × 6 = 60.
Cut-out piece: 4 × 3 = 12.
Subtract.
The answer is 48.
Where students go wrong
Adding the cut-out piece instead of subtracting it. A missing corner makes the area smaller.
Also called compound shapes, irregular figures, shaded regions or area of composite shapes.
What you can put on this worksheet
Area of a composite figure
What is the area of the shaded region? — a rectangle with a rectangular hole, the border shaded, labeled 12, 10, 7, 4→ 92
Perimeter of a composite figure
Find the perimeter. — an l-shaped figure, labeled 14, 11, 10, 2→ 50
Shaded regions with circles
A shape is a 3 by 14 rectangle with a semicircle of diameter 14 on one of its 14 sides. Find its area.→ 42+249π
Perimeters with semicircles
A quarter circle has radius 13. Find the perimeter of the quarter circle (both straight edges and the arc).→ 26+213π
Questions about these worksheets
Yes. Every area of composite figures sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the area of composite figures questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 4: area of a composite figure, perimeter of a composite figure, shaded regions with circles and perimeters with semicircles. Tick as many as you want and set how many of each, or let it spread them evenly.
Adding the notch instead of subtracting it, and on a semicircle, forgetting to halve the circle.