Area of Composite Figures
Combining triangles with other shapes to find total area
1. What are Composite Figures?
A composite figure is made up of two or more simple shapes combined together.
Common Combinations:
Square + Triangle
(House shape)
Rectangle + Triangle
(Arrow shape)
Square + Triangle
(Trapezium)
2. Two Methods to Find Area
Method 1: Split and Add
- Split into simple shapes
- Find area of each shape
- Add all areas together
Total = Area A + Area B
Method 2: Take Away
- Start with a larger shape
- Find area of the larger shape
- Subtract the removed part
Total = Big Area − Removed Area
💡 Which Method to Use?
Both methods give the same answer! Choose the one that seems easier for each problem.
3. Worked Examples
Example 1: Trapezium (Split and Add)
In trapezium PTRS, the angles at P and S are right angles. PT = 6 cm, PS = 6 cm and SR = 10 cm. Find the area of the trapezium.
ShowHide solution
Split and Add Method:
Step 1: Draw the line TU perpendicular to SR. It splits the trapezium into square PTUS and triangle TRU
Step 2: Area of square PTUS = 6 × 6 = 36 cm²
Step 3: RU = 10 − 6 = 4 cm
Area of triangle TRU = ½ × 4 × 6 = 12 cm²
Step 4: Total area = 36 + 12 = 48 cm²
Example 2: House Shape (Square + Triangle)
EFGH is a square with side 8 cm. Triangle EFK has height 2 cm. Find the total area of the figure.
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Solution:
Area of square EFGH = 8 × 8 = 64 cm²
Area of triangle EFK = ½ × 8 × 2 = 8 cm²
Total area = 64 + 8 = 72 cm²
4. Practice Questions
Practice 1:
ABCD is a square drawn on a grid of 1-cm squares. Find the area of the shaded triangle.
ShowHide answer
Take Away Method:
Area of Square ABCD = 4 × 4 = 16 cm²
Area of Triangle P = ½ × 1 × 4 = 2 cm²
Area of Triangle Q = ½ × 3 × 2 = 3 cm²
Area of Triangle R = ½ × 4 × 2 = 4 cm²
Area of shaded triangle = 16 − 2 − 3 − 4
= 7 cm²
Practice 2:
ABCD is a rectangle with length 30 cm and breadth 16 cm. Find the area of the shaded triangle.
ShowHide answer
Base of triangle = AB = 30 cm
Height of triangle = AD = BC = 16 cm (opposite sides of a rectangle are equal)
Area of triangle = ½ × 30 × 16 = ½ × 480
= 240 cm²
Practice 3:
The figure is made up of triangle A, rectangle B and rectangle C. Triangle A has base 5 cm and height 3 cm. Rectangle B measures 15 cm by 5 cm. Rectangle C measures 5 cm by 3 cm. Find the area of the figure.
ShowHide answer
Split and Add Method:
Area of triangle A = ½ × 5 × 3 = 7.5 cm²
Area of rectangle B = 15 × 5 = 75 cm²
Area of rectangle C = 5 × 3 = 15 cm²
Area of figure = 7.5 + 75 + 15
= 97.5 cm²
Key Takeaways
- Composite figures are made of two or more simple shapes
- Split and Add: Divide into shapes, find each area, then add
- Take Away: Start with larger shape, subtract removed parts
- Always identify the simple shapes first before calculating
- Label your shapes (A, B, C) to keep track of your work
- Both methods give the same answer - choose whichever is easier!