Area of Compound Shapes

In a Nutshell

Split a compound shape into simpler shapes you already know — rectangles, triangles, or trapeziums — then add (or subtract) their areas.

A compound shape (sometimes called a composite shape) is made from two or more simpler shapes joined together. To find the total area:

  1. Identify a sensible way to split the shape.
  2. Work out the dimensions of each part.
  3. Calculate the area of each part using the correct formula.
  4. Add the areas together.
Total area=AreaA+AreaB+…\text{Total area} = \text{Area}_A + \text{Area}_B + \dots

Sometimes it is easier to start with a larger rectangle and subtract the missing piece.

Explore: decompose an L-shape

Compound shape decomposition An L-shaped compound shape split into two rectangles to find the total area. A B 5 cm 3 cm 8 cm 3 cm

Press Split shape to separate the L-shape into two rectangles and see each area calculated.

Watch it work

Question: An L-shaped room has the overall dimensions 8 m×6 m8 \, \text{m} \times 6 \, \text{m}, with a 3 m×4 m3 \, \text{m} \times 4 \, \text{m} rectangular piece cut from the top-right corner. Find the floor area.

Have a go

Q1. A T-shape is made from a 6×26 \times 2 rectangle on top and a 2×52 \times 5 rectangle below. Find the total area (all in cm).

Q2. A rectangular garden measures 10 m×7 m10 \, \text{m} \times 7 \, \text{m}. A square pond of side 2 m2 \, \text{m} is in the middle. What area of garden remains?

Q3. An L-shape is formed by two rectangles: 5×35 \times 3 and 7×37 \times 3 (cm). Find the total area.

Q4. A shape is made from a rectangle 8×4 cm8 \times 4 \, \text{cm} with a right-angled triangle (base 4 cm4 \, \text{cm}, height 3 cm3 \, \text{cm}) on top. Find the total area.