Area and Perimeter
Perimeter is the distance around a shape — add up all the sides. Area is the amount of space inside — measured in square units. Both show up constantly in real life: fencing a yard (perimeter), buying carpet (area), planning a garden (both).
Key Concepts
Perimeter of Common Shapes
Rectangle: P = 2l + 2w. Square: P = 4s. Triangle: add all three sides. Irregular shapes: add every side. Units stay the same as the side lengths (feet, meters, inches).
Area of Rectangles and Squares
Area = length × width. A room 12 ft × 15 ft = 180 sq ft of carpet needed. Square: A = s². Units are always squared (ft², m², in²). Area doubles if you double one side; it quadruples if you double both.
Area of Triangles and Compound Shapes
Triangle: A = ½ × base × height. The height must be perpendicular (90°) to the base. Compound shapes: break into rectangles and triangles, find each area separately, then add (or subtract for holes). Always label your sketch!
🆕 Shape Calculator
Click a shape to calculate its area and perimeter.
✅ Check Your Understanding
1. What is the area of a rectangle 9 ft × 4 ft?
2. What formula gives the area of a triangle?
3. Perimeter measures...