Finding Area of Compound Figures

Compound figures (also called composite figures) are shapes made by combining two or more simple shapes such as rectangles, triangles, or semicircles. To find the area of a compound figure, you break it into simpler pieces, find each area separately, and then add (or subtract) the results. This skill appears frequently on the GED Math test, and with a clear strategy it becomes completely manageable.

What Is a Compound Figure?

A compound figure is any flat shape that cannot be classified as a single standard polygon. An L-shape, a T-shape, or a rectangle with a triangular notch cut out are all examples. Because every compound figure is built from basic shapes, the formulas you already know for rectangles, triangles, circles, and parallelograms are all you need.

GED Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the GED Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.33 out of 5 based on 105 customer ratings

Satisfied 91 Students

How to Find the Area of Compound Figures

Method 1: Addition (Combining Shapes)

Divide the compound figure into non-overlapping simpler shapes, find the area of each, and add them together.

Total \(\color{blue}{\text{ Area } = \text{ Area }}\)₁ + Area₂ + …

Method 2: Subtraction (Removing a Piece)

Sometimes it is easier to start with a large simple shape and subtract the area of the missing piece.

Total \(\color{blue}{\text{ Area } = \text{ Area }}\) of large \(\color{blue}{\text{ shape } – \text{ Area }}\) of removed piece

Key Formulas

• Rectangle: \(\color{blue}{A = l \times w}\)
• Triangle: A = ½ × \(\color{blue}{b \times h}\)
• Circle / Semicircle: A = πr² (full circle) or ½πr² (semicircle)
• Parallelogram: \(\color{blue}{A = b \times h}\)

Step-by-Step Summary

1. Look at the compound figure and identify the simpler shapes inside it.
2. Decide whether to add (combining pieces) or subtract (removing a cutout).
3. Label all needed dimensions from the diagram.
4. Calculate the area of each simple shape using the correct formula.
5. Add or subtract the individual areas to get the total area.
6. State the answer with the correct square units.

Watch: Finding the Perimeter and Area of a Composite Shape (Video Lesson)

Math with Mr. J walks through an L-shaped example step by step:

Worked Examples

Example 1: Find the area of an L-shaped figure with outer dimensions 10 \(\color{blue}{\text{ ft } \times 8}\) ft, with a 4 \(\color{blue}{\text{ ft } \times 3}\) ft rectangle removed from the upper-right corner.

Step 1: Area of full \(\color{blue}{\text{ rectangle } = 10 \times 8 = 80}\) ft²
Step 2: Area of removed \(\color{blue}{\text{ piece } = 4 \times 3 = 12}\) ft²
Step 3: Total \(\color{blue}{\text{ area } = 80 – 12}\) = 68 ft²

Example 2: A figure is made of a 6 \(\color{blue}{m \times 4}\) m rectangle topped with a semicircle of diameter 4 m (radius 2 m).

Step 1: Area of \(\color{blue}{\text{ rectangle } = 6 \times 4 = 24}\) m²
Step 2: Area of semicircle = ½ × π × 2² ≈ 6.28 m²
Step 3: Total area ≈ \(\color{blue}{24 + 6.28}\) = 30.28 m²

Example 3: Find the area of a 12 \(\color{blue}{\text{ in } \times 5}\) in rectangle with a 3 \(\color{blue}{\text{ in } \times 2}\) in rectangular notch removed.

\(\color{blue}{\text{ Area } = 12 \times 5 – 3 \times 2 = 60 – 6}\) = 54 in²

Example 4: A T-shape has a top bar 8 \(\color{blue}{\text{ cm } \times 2}\) cm and a vertical stem 2 \(\color{blue}{\text{ cm } \times 5}\) cm.

\(\color{blue}{\text{ Area } = (8 \times 2) + (2 \times 5) = 16 + 10}\) = 26 cm²

More Practice: Area of Composite Figures (Video)

This video works through additional composite figure examples with clear step-by-step explanations:

Exercises

1. An L-shape has outer dimensions 9 \(\color{blue}{\text{ ft } \times 6}\) ft with a 3 \(\color{blue}{\text{ ft } \times 3}\) ft square removed from one corner. Find the area.
2. A rectangle 7 \(\color{blue}{m \times 5}\) m has a right triangle with base 3 m and height 4 m attached to one end. Find the total area.
3. A figure is a 10 \(\color{blue}{\text{ cm } \times 8}\) cm rectangle with a 4 \(\color{blue}{\text{ cm } \times 2}\) cm cutout. Find the area.
4. A compound shape consists of two rectangles: one 6 \(\color{blue}{\text{ in } \times 4}\) in and one 6 \(\color{blue}{\text{ in } \times 3}\) in placed end to end. Find the total area.
5. A window is a 12 \(\color{blue}{\text{ ft } \times 3}\) ft rectangle topped by a 4 \(\color{blue}{\text{ ft } \times 4}\) ft square. Find the total area.

Answers

1. \(\color{blue}{9 \times 6 – 3 \times 3 = 54 – 9}\) = 45 ft²
2. \(\color{blue}{7 \times 5}\) + ½ × \(\color{blue}{3 \times 4 = 35 + 6}\) = 41 m²
3. \(\color{blue}{10 \times 8 – 4 \times 2 = 80 – 8}\) = 72 cm²
4. \(\color{blue}{6 \times 4 + 6 \times 3 = 24 + 18}\) = 42 in²
5. \(\color{blue}{12 \times 3 + 4 \times 4 = 36 + 16}\) = 52 ft²

The Ultimate Elementary School Math Bundle Grade 3-5

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Frequently Asked Questions

What is a compound figure in math?

A compound (or composite) figure is a shape formed by two or more basic geometric shapes joined together or with a piece removed. Examples include L-shapes, T-shapes, and rectangles with triangular cutouts.

How do you find the missing side lengths of a compound figure?

Use the fact that opposite sides of rectangular regions are equal. For an L-shape, the missing horizontal side equals the total width minus the known horizontal piece; the missing vertical side equals the total height minus the known vertical piece.

Do I always add areas when working with compound figures?

No. If a piece is cut out of a larger shape, you subtract. If shapes are joined together, you add. The key is correctly identifying whether each piece is added or removed.

Related Topics

• Area of a Triangle
• Area of a Parallelogram
• Area of a Trapezoid
• Polygons
• Rectangular Prisms
• Cubes