Math with Mr. J: Finding the Area of Composite Figures

Key Concepts

Composite Figure: A shape that can be divided into simpler shapes (e.g., rectangles, squares) whose areas we can calculate easily.
Strategy: Break down the composite figure into known shapes, calculate each area, and sum these areas to get the total area of the composite figure.

Dividing the Figure:
- Separate the figure into two rectangles.
- Draw a dashed line to indicate the division.
- Label the left rectangle as "A" and the right rectangle as "B".
Calculating Area:
- Rectangle A:
  - Formula: Area = Length x Width
  - Length = 8 (whole height), Width = 3
  - Area = 8 x 3 = 24 square inches
- Rectangle B:
  - Formula: Area = Length x Width
  - Length = 2, Width = 7 (not 10 since it’s the full width)
  - Area = 2 x 7 = 14 square inches
Total Area:
- Add areas of A and B: 24 + 14 = 38 square inches
- Note: Alternative ways to divide (e.g., top and bottom rectangle) can be used.

Dividing the Figure:
- Separate into three shapes: two rectangles and one square.
- Label them as "A", "B", and "C".
Calculating Area:
- Rectangle A:
  - Formula: Area = Length x Width
  - Length = 5 cm, Width = 2 cm
  - Area = 5 x 2 = 10 square centimeters
- Rectangle B:
  - Missing measurement for length,
  - Total height = 5 cm, Part of it = 3 cm
  - Length = 5 - 3 = 2 cm, Width = 3 cm
  - Area = 2 x 3 = 6 square centimeters
- Square C:
  - Formula: Area = Length x Width
  - Length = 5 cm, Width = 5 cm (it's a square)
  - Area = 5 x 5 = 25 square centimeters
Total Area:
- Add areas of A, B, and C: 10 + 6 + 25 = 41 square centimeters
- Note: Similar to example 1, multiple solving methods can be used, focus on correct measurements for lengths and widths.

Breaking down composite figures into simpler shapes is crucial for calculating area.
Always verify the dimensions used for length and width to ensure accuracy.

Thanks for watching and see you next time!