Sometimes a picture has a colored (shaded) part and a white (unshaded) part. You're asked: "What is the area of the shaded part?"
The trick: don't try to measure the weird shaded shape directly. Instead, work with the simple shapes hiding inside the picture!
📖 Recipe: Subtract the Hole
Find the area of the big outer shape.
Find the area of the white (unshaded) shape inside.
Subtract: Shaded = Big − White.
Shaded Area = Outer Area − Inner Area
Worked Example: Rectangle with a Square Hole
A 20 cm × 10 cm rectangle has a 6 cm × 6 cm square cut out. Find the shaded area.
Step 1: Outer area = 20 × 10 = 200 cm²
Step 2: Inner area = 6 × 6 = 36 cm²
Step 3: Shaded = 200 − 36 = 164 cm² ✓
Worked Example: Rectangle with a Triangle Hole
A 12 cm × 4 cm rectangle has a triangle (base 9 cm, height 4 cm) cut out. Find the shaded area.
Step 1: Outer rectangle = 12 × 4 = 48 cm²
Step 2: Triangle = (9 × 4) ÷ 2 = 36 ÷ 2 = 18 cm²
Step 3: Shaded = 48 − 18 = 30 cm² ✓
🎨 Area of Shaded Regions
Another strategy: add the pieces ➕
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💡 When the Shape Is Made of Pieces
Sometimes the shaded region is built up from simpler shapes — like an L-shape made from two rectangles. Then you don't subtract — you add!
📖 Recipe: Add the Pieces
Split the shape into rectangles, squares, triangles, or parallelograms.
Find the area of each piece.
Add them together.
Worked Example: An L-Shape
An L-shape splits into rectangle A (8 cm × 6 cm on top) and rectangle B (16 cm × 6 cm on bottom).
Step 1: Area of A = 8 × 6 = 48 cm²
Step 2: Area of B = 16 × 6 = 96 cm²
Step 3: Total shaded = 48 + 96 = 144 cm² ✓
💡 Tip: Sometimes either method works! You can split an L-shape into 2 rectangles (add) OR you can imagine the full big rectangle and subtract the missing corner (subtract). Try both and check your answer matches!
L-shape: piece A = 5 × 3, piece B = 8 × 4
A = B =
Total =
T-shape: top 10 × 2, stem 4 × 6
Top = Stem =
Total =
3 Word Problems 📝
Decide whether to subtract or add!
A rectangular rug is 6 m by 4 m. In the middle there is a square table covering a 2 m × 2 m patch. What area of the rug is still showing?
Shaded area = m²
A wall is a 10 m × 3 m rectangle. A 2 m × 1 m window is cut into it. How many m² of the wall need painting?
Painted area = m²
Picture problems — find the shaded area from the diagram! 🖼️
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👀 Read the Picture Carefully
For each picture: the shaded (colored) part is what you want to find. Look at the dimensions on the outside, find the area of the whole outer shape, find the area of the white shape inside, and subtract.
4 Find the Shaded Area 🖼️
Each picture shows a rectangle with a white shape cut out. Use the dimensions to find the shaded area.