What you’ll learn
Area of composite figures.
Key idea
A triangle uses half its base times perpendicular height; sharing a boundary edge does not create overlapping area.
Only boundary is shared, not interior; a triangular region requires half its base-height product, and missing height follows subtraction of rectangle area.
Worked example
Enter the exact value or ordered values in the format requested below.
A house-shaped region is a 2cm-wide rectangle of height 3cm with a triangle attached along its top edge, base 2cm and perpendicular height 6cm. Interiors do not overlap. Enter total area as a number of square cm.
- The rectangle area is 2×3=6cm²; attached triangle area is (2×6)/2=6cm².
- The interiors do not overlap, so add these areas: 6+6=12cm².
Answer: 12
Quick Check
Evaluate a worked attempt at area of composite figures, identify the first invalid step, and provide the correction.
Composite region: rectangle 2×5cm, nonoverlapping attached triangle base 2cm,height 9cm. Step1: rectangle area=10cm². Step2: triangle area=18cm² without halving. Locate the first invalid step and correct total.