Lesson
7
Composite 2D Shapes
Learning Intent: Calculate areas of simple and composite 2D shapes.
Key Strategy: Splitting & Subtracting
To find the area of a complex shape, split it into regions you know (Rectangles, Triangles, Circles).
Example: L-Shape
$$Area_{Total} = Area_{Rect1} + Area_{Rect2}$$
QUIZ Test Yourself
- Find the area of a square with side length $5\text{cm}$.
- Calculate the area of a rectangle ($10\text{m} \times 4\text{m}$) with a square hole ($2\text{m} \times 2\text{m}$) cut out.
Show Answers
1. $A = 5 \times 5 = 25\text{cm}^2$
2. Rectangle: $40\text{m}^2$, Hole: $4\text{m}^2$. Total: $36\text{m}^2$.
Practice Problem 7.1
A "House Profile" shape has a rectangular base ($12\text{m} \times 8\text{m}$) and a triangular roof with a vertical height of $5\text{m}$.
Calculate the total area:
Solution: $(12 \times 8) + (0.5 \times 12 \times 5) = 126\text{m}^2$