Area and Perimeter of Plane Figures
Understanding area and perimeter is essential in geometry, as they help us measure the size and boundary of different shapes. Here’s a detailed explanation of common 2D figures:
1. Rectangle
- Area: Length × Width
- Perimeter: 2 × (Length + Width)
- Properties: Opposite sides are equal; all angles are 90 degrees.
2. Square
- Area: Side × Side
- Perimeter: 4 × Side
- Properties: All sides are equal; all angles are 90 degrees.
3. Triangle
- Area: 1/2 × Base × Height
- Perimeter: Sum of all sides
- Properties: Sum of angles is 180 degrees; can be classified as equilateral, isosceles, or scalene.
4. Circle
- Area: π × Radius²
- Perimeter (Circumference): 2 × π × Radius
- Properties: All points are equidistant from the center; no angles.
5. Trapezoid
- Area: 1/2 × (Base1 + Base2) × Height
- Perimeter: Sum of all sides
- Properties: At least one pair of parallel sides.
6. Parallelogram
- Area: Base × Height
- Perimeter: 2 × (Base + Side)
- Properties: Opposite sides are equal and parallel; opposite angles are equal.
Key Takeaways
- Area measures the space inside a shape.
- Perimeter measures the distance around a shape.
- Different shapes have unique formulas for calculating area and perimeter.
Understanding these concepts is fundamental in solving various problems in geometry, and they form the basis for more complex mathematics.