What is a composite figure?

A shape made by joining two or more simple shapes, such as rectangles, triangles or half circles. An L-shape is the most common example.

How do you find the area of a composite figure?

Split it into simple shapes, find the area of each and add them. Or find the area of a big rectangle around it and subtract the missing parts.

How do you find the area of an L-shape?

Split it into two rectangles and add their areas, or subtract the missing corner from the full rectangle. A 12 m by 10 m rectangle with a 7 m by 6 m corner missing has an area of 120 − 42 = 78 m².

How do you find missing sides on a composite figure?

Use opposite sides. The short edges on one side add up to the long edge opposite them. If the bottom is 12 m and the top is 5 m, the missing step is 12 − 5 = 7 m.

Is a composite figure the same as a compound shape?

Yes. Composite figure, composite shape and compound shape all mean a shape made from simpler shapes. US textbooks usually say composite figure, and schools in England often say compound shape.

What grade learns the area of composite figures?

In the US, it starts in grade 3 with rectangles (3.MD.C.7.d), adds triangles in grade 6 (6.G.A.1) and circles in grade 7 (7.G.B.4, 7.G.B.6). In England, rectilinear shapes come in Years 4 and 5, and composite shapes with circles in Key Stage 3.

Is there a free area of composite figures worksheet with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 3 to 7 (Years 4 to 8 in England)

Area of composite figures: split, add or subtract

Here is how to find the area of a composite figure, also called a composite or compound shape: split it into rectangles and triangles, or start with a big rectangle and take away what is missing. Try the free practice below, then print a fresh area of composite shapes worksheet with an answer key.

The method, step by step

Decide how to break the figure into simple shapes: rectangles, triangles or half circles.
Work out any missing side lengths from the sides you know.
Find the area of each simple shape.
Add the areas of the pieces, or subtract the area of any piece that is cut out.
Write the answer in square units, and check it by splitting the figure a different way.

CCSS 3.MD.C.7.DCCSS 6.G.A.1CCSS 7.G.B.4England: Y5 MeasurementEngland: Y6 MeasurementEngland: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures

Worked example

An L-shaped room has a bottom wall of 12 m and a left wall of 10 m. The top wall is 5 m and the right wall is 4 m. The other two walls are not labeled. Find the floor area.

The unlabeled horizontal wall is 12 − 5 = 7 m, and the unlabeled vertical wall is 10 − 4 = 6 m.
Split the room with a vertical line into a tall rectangle, 5 m by 10 m, and a short one, 7 m by 4 m.
Tall part: 5 × 10 = 50 m². Short part: 7 × 4 = 28 m².
Add them: 50 + 28 = 78 m².
Check by subtracting: the full 12 m by 10 m rectangle is 120 m², and the missing corner is 7 m by 6 m, which is 42 m². 120 − 42 = 78 m².
The floor area is 78 m².

Practice now

Question 1 of 100 correct

A window is a 6 dm by 10 dm rectangle with a semicircle on top (the semicircle's diameter is the 6 dm side). Find the total area of glass in dm², to 1 decimal place.

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What a composite figure is

A composite figure, also called a composite shape or compound shape, is made from two or more simple shapes joined together. An L-shaped room, a house shape (a rectangle with a triangle on top) and an arched window (a rectangle with a half circle on top) are all composite figures.

There is no single formula for them. Instead, you break the figure into shapes you already know, find each area and combine them. This works because area adds up: the area of the whole is the sum of the areas of its parts, as long as the parts do not overlap.

Two ways to find the area

Split and add: cut the figure into rectangles or triangles that do not overlap, find each area and add them.
Surround and subtract: draw a big rectangle around the whole figure, find its area, then subtract the area of the parts that are missing.

Both ways give the same answer, so using one to check the other catches most slips. Splitting is usually easier for a T-shape or a plus sign. Subtracting is usually easier for an L-shape or a frame with a hole in it.

Finding missing lengths

Composite figures often leave some sides unlabeled. Use the fact that opposite sides of a rectangle are equal. In an L-shape, the two short horizontal edges together equal the long bottom edge, and the two short vertical edges together equal the long side edge. If the bottom is 12 m and the top is 5 m, the step must be 12 − 5 = 7 m.

Write each length on the drawing as you find it. Most mistakes with composite area come from using a side that belongs to a different rectangle.

Area of composite shapes: examples

These examples get a little harder each time.

Two rectangles: a garden made of a 6 ft by 4 ft bed and a 3 ft by 5 ft bed has an area of 24 + 15 = 39 ft².
A rectangle with a hole: a 10 m by 8 m lawn with a 3 m by 2 m flower bed cut out of it has 80 − 6 = 74 m² of grass.
A rectangle and a triangle: a house-shaped sign is a rectangle 10 cm wide and 6 cm tall, with a triangle on top that is 10 cm wide and 4 cm tall. The area is 10 × 6 + ½ × 10 × 4 = 60 + 20 = 80 cm².
A path around a pond: an 8 m by 5 m pond has a path 1 m wide all the way around it. The outer rectangle is 10 m by 7 m, so the path covers 70 − 40 = 30 m².
A rectangle and a half circle: a window is a 6 dm by 8 dm rectangle with a semicircle on the 6 dm side. The semicircle has a radius of 3 dm, so its area is ½ × π × 3² ≈ 14.1 dm², and the total is about 48 + 14.1 = 62.1 dm².

How it is taught in school

In the US, Common Core introduces composite area in grade 3: students find the area of rectilinear figures by splitting them into rectangles and adding the areas (3.MD.C.7.d). Grade 6 adds triangles and other polygons, found by composing rectangles or splitting into triangles (6.G.A.1). Grade 7 solves real problems with composite shapes (7.G.B.6) and brings in circles (7.G.B.4).

In England, Year 4 pupils find the area of rectilinear shapes by counting squares. Year 5 pupils calculate the area of rectangles in cm² and m² and the perimeter of composite rectilinear shapes. Year 6 adds the area of triangles and parallelograms, and Key Stage 3 covers the area of circles and composite shapes.

How parents can help

Use squared paper. Draw an L-shape, count the squares, then check by splitting it into two rectangles.
Measure an L-shaped room, patio or garden at home and find its area both ways.
Ask your child to label every side before finding any areas, including the sides that were not given.
Encourage a quick sketch for word problems. A drawing with the lengths marked makes the pieces easy to see.
Keep sessions short. Print a fresh worksheet, let your child mark it with the answer key, and go through the worked steps for any they missed.

Common mistakes

Using a side from the wrong rectangle. In the L-shaped room, the short part is 7 m by 4 m, not 12 m by 4 m, which would count part of the tall rectangle twice.
Letting the pieces overlap. When you split a figure, every square should belong to exactly one piece, or the area comes out too big.
Adding when you should subtract. A 10 m by 8 m lawn with a 3 m by 2 m bed cut out has 80 − 6 = 74 m² of grass, not 86 m².
Forgetting the ½ for a triangle. A triangle with a base of 10 cm and a height of 4 cm has an area of 20 cm², not 40 cm².
Finding the perimeter by mistake. Area counts the squares inside, in cm² or m²; perimeter is the distance around the edge.
Mixing units in one figure. Change every length to the same unit, such as all meters or all centimeters, before multiplying.

Questions people ask

What is a composite figure?: A shape made by joining two or more simple shapes, such as rectangles, triangles or half circles. An L-shape is the most common example.
How do you find the area of a composite figure?: Split it into simple shapes, find the area of each and add them. Or find the area of a big rectangle around it and subtract the missing parts.
How do you find the area of an L-shape?: Split it into two rectangles and add their areas, or subtract the missing corner from the full rectangle. A 12 m by 10 m rectangle with a 7 m by 6 m corner missing has an area of 120 − 42 = 78 m².
How do you find missing sides on a composite figure?: Use opposite sides. The short edges on one side add up to the long edge opposite them. If the bottom is 12 m and the top is 5 m, the missing step is 12 − 5 = 7 m.
Is a composite figure the same as a compound shape?: Yes. Composite figure, composite shape and compound shape all mean a shape made from simpler shapes. US textbooks usually say composite figure, and schools in England often say compound shape.
What grade learns the area of composite figures?: In the US, it starts in grade 3 with rectangles (3.MD.C.7.d), adds triangles in grade 6 (6.G.A.1) and circles in grade 7 (7.G.B.4, 7.G.B.6). In England, rectilinear shapes come in Years 4 and 5, and composite shapes with circles in Key Stage 3.
Is there a free area of composite figures worksheet with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 4, 2026.

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