What you’ll learn
Find polygon area by decomposition.
Key idea
The removed region reduces the area; its two dimensions are not perimeter deductions.
The cutout is absent, so subtract its area; recovering one cutout dimension requires using the cutout area, not the remaining polygon area.
Worked example
Enter the exact value or ordered values in the format requested below.
An L-shaped polygon is a 6-by-7 cm rectangle with a 4-by-2 cm upper-right corner cut out. Enter its numerical area in square centimeters.
- The full enclosing rectangle has area 6×7=42 cm²; its removed corner has area 4×2=8 cm².
- The remaining L shape has area 42-8=34 cm².
Answer: 34
Quick Check
Evaluate a worked attempt at find polygon area by decomposition, identify the first invalid step, and provide the correction.
For an L shape formed by a 6-by-10 rectangle minus a 3-by-3 corner, a student writes Step 1: outer area 60. Step 2: cutout area 9. Step 3: remaining area 60+9=69. Locate the first invalid step and correct it.