5B Composite Figures Study Guide

Key Vocabulary

Composite Figure — a shape made of two or more basic shapes combined together. (figura compuesta)

Decompose — to break apart a composite figure into smaller, basic shapes. (descomponer)

Irregular Shape — a shape that is not a standard rectangle, triangle, etc. (forma irregular)

Area — the space inside a flat shape, measured in square units. (área)

Visual Example

An L-shaped figure can be split into two rectangles:

  +-------+
  |       |  3 ft
  |   A   |
  +---+---+---+
      |       |  4 ft
      |   B   |
      +-------+
   4ft   6 ft

Shape A: 4 × 3 = 12 sq ft
Shape B: 6 × 4 = 24 sq ft
Total Area = 12 + 24 = 36 sq ft

Sometimes you SUBTRACT instead of adding:

  +-------------+
  |             |  8 ft
  |    +---+    |
  |    | X |    |  2 ft (cut out)
  |    +---+    |
  |             |
  +-------------+
      10 ft

Big rectangle: 10 × 8 = 80 sq ft
Cut-out (X):    3 × 2 =  6 sq ft
Shaded Area = 80 − 6 = 74 sq ft

Step-by-Step

1 Look at the figure. Draw lines to break it into basic shapes (rectangles, triangles, etc.).
2 Find the area of each basic shape using the correct formula.
3 Add the areas together if the shapes are joined, or subtract if a piece is cut out.
4 Write your answer in square units.

Formula Box

Composite Area = Area of Shape 1 + Area of Shape 2 + ...

Or: Composite Area = Total Area − Cut-out Area

Watch Out!

Don’t double-count shared edges. When two shapes share a side, that length is already included in both calculations — just add the areas.
Sometimes you SUBTRACT. If a shape has a piece cut out (like a hole), subtract the missing area.
Find missing dimensions. You may need to subtract lengths to find a side that isn’t labeled.
There is often more than one way to break up a shape. Any correct way gives the same total area.

Practice Problems

1. An L-shape is made of two rectangles. Rectangle A is 5 cm × 3 cm. Rectangle B is 4 cm × 6 cm. What is the total area?

2. A large rectangle is 12 ft × 8 ft. A square with side 3 ft is cut out of it. What is the remaining area?

3. A shape is made of a rectangle (8 m × 5 m) with a triangle on top (base 8 m, height 3 m). What is the total area?