Overview
This lecture explains how to find the area of composite figures by breaking them into simpler shapes and adding their individual areas.
Composite Figures and Strategy
- A composite figure is a shape made from two or more simple shapes (e.g., rectangles, squares).
- To find its area, separate the figure into simpler shapes whose areas are easier to calculate.
- Find the area of each simple shape, then add those areas together for the total.
Example 1: Two Rectangles
- Split the figure into rectangle A and rectangle B.
- Area formula for a rectangle: Area = length × width.
- For rectangle A: length = 8 inches, width = 3 inches; Area = 24 square inches.
- For rectangle B: length = 2 inches, width = 7 inches; Area = 14 square inches.
- Total area = 24 + 14 = 38 square inches.
- You can split composite figures in different ways, but always choose correct measurements for length and width.
Example 2: Three Rectangles (including a Square)
- Split the figure into shapes A, B, and C (two rectangles, one square).
- For shape A: length = 5 cm, width = 2 cm; Area = 10 square cm.
- For shape B: must deduce missing length; given height is 5 cm and one segment is 3 cm, so the other must be 2 cm; Area = 2 × 3 = 6 square cm.
- For shape C: a square with length and width = 5 cm; Area = 25 square cm.
- Total area = 10 + 6 + 25 = 41 square cm.
- Sometimes you need to calculate missing dimensions using the total lengths or heights given.
Key Terms & Definitions
- Composite Figure — A shape made up of two or more simple shapes.
- Area — The amount of space inside a shape, measured in square units.
- Rectangle Area Formula — Area = length × width.
Action Items / Next Steps
- Practice separating composite figures into simple shapes and finding their total area.
- Be careful to use correct measurements for each simple shape.
- Prepare for exercises where you may need to deduce missing dimensions.