Area — Grade 5 Mathematics
In Grade 5, we extend our area skills to include parallelograms and compound shapes that combine triangles, rectangles, and parallelograms.
Area Formulae
Parallelogram — Why base × height?
The perpendicular height is the vertical distance between the parallel sides — not the slanted side length!
Compound Shapes — Split and Add
Strategy: Split the compound shape into simpler shapes (rectangles and triangles). Find each area separately, then add (or subtract) them.
- Identify the simpler shapes
- Label the relevant measurements
- Calculate each area
- Add (or subtract) to find total area
Worked Examples
A parallelogram has base 12 cm and perpendicular height 9 cm. Find its area.
- A = base × height = 12 × 9 = 108 cm²
A shape consists of a rectangle 10 cm × 6 cm, with a triangle on top (base 10 cm, height 4 cm).
- Rectangle area = 10 × 6 = 60 cm²
- Triangle area = ½ × 10 × 4 = 20 cm²
- Total = 60 + 20 = 80 cm²
A large rectangle 14 cm × 10 cm has a rectangular notch cut out, 4 cm × 3 cm. Find the remaining area.
- Large rectangle = 14 × 10 = 140 cm²
- Notch = 4 × 3 = 12 cm²
- Remaining area = 140 − 12 = 128 cm²
Practice Questions
1. Find the area of a parallelogram with base 15 cm and perpendicular height 8 cm.
2. A triangle has base 14 cm and perpendicular height 11 cm. Find its area.
3. A compound shape is made of a 9 cm × 4 cm rectangle joined to a 9 cm × 5 cm rectangle. Find the total area.
4. A large rectangle is 20 cm × 15 cm. A triangular section with base 20 cm and height 6 cm is removed from the top. Find the remaining area.
5. A parallelogram has area 90 cm² and base 18 cm. Find its perpendicular height.
Key Points to Remember
- Parallelogram area = base × perpendicular height (not the slant side).
- Triangle area = ½ × base × perpendicular height.
- For compound shapes: split into simple shapes, then add or subtract their areas.
- Label each separate part and its dimensions clearly before calculating.
- Area is always measured in square units (cm², m², mm²).