Area — Grade 3 Mathematics
In Grade 3, we find the area of compound (composite) shapes by splitting them into rectangles, calculating each part, and adding (or subtracting) the parts together.
Area of Compound Shapes
Method 1 — Split and Add: Divide the shape into separate rectangles, find each area, then add.
Method 2 — Whole minus Hole: Find the area of the full outer rectangle, then subtract the missing piece.
Split and Add — L-Shape Example
Worked Examples
An L-shape: top part is 8 cm × 4 cm; bottom part is 3 cm × 5 cm. Find the total area.
- Area A = 8 × 4 = 32 cm²
- Area B = 3 × 5 = 15 cm²
- Total = 32 + 15 = 47 cm²
A rectangle 10 cm × 7 cm has a 4 cm × 3 cm rectangular hole cut from one corner. Find the remaining area.
- Full rectangle: 10 × 7 = 70 cm²
- Hole: 4 × 3 = 12 cm²
- Remaining = 70 − 12 = 58 cm²
A garden is 12 m × 8 m. A square pond (3 m × 3 m) sits in one corner. What is the lawn area?
- Garden area = 12 × 8 = 96 m²
- Pond area = 3 × 3 = 9 m²
- Lawn = 96 − 9 = 87 m²
Practice Questions
1. Find the area: rectangle A = 9×5 cm, rectangle B = 4×3 cm, joined together.
2. A 10×10 square has a 2×3 piece removed. Find the remaining area.
3. An L-shape: outer rectangle 12×8 m, cut-out 4×5 m. What is the L-shape area?
4. A floor plan is made of two rectangles: 6×4 m and 3×2 m. How many 1 m² tiles are needed?
5. A rectangle is 8 m × 6 m. Its area is split equally between two children. How much does each get?
Key Points to Remember
- Compound shape: split into rectangles, find each area, then add.
- Alternative: whole rectangle minus the missing piece.
- Draw a diagram and label all dimensions before calculating.
- Area is in square units (cm², m²).
- A missing side of a compound shape uses the same logic as missing sides in perimeter problems.