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Definition of Quadrilaterals

• Quadrilaterals are defined as figures that have four sides and four angles.

Types of Quadrilaterals

• The main types of quadrilaterals include:

  • Square

  • Rectangle

  • Parallelogram

  • Trapezoid

  • Rhombus

Perimeter of Quadrilaterals

• The perimeter of a quadrilateral is the total length of all its sides.

• Formulas for Perimeter:

  • Square or Rhombus:

  • Formula: ext{Perimeter} = 4 imes ext{length of one side}

  • Rectangle or Parallelogram:

  • Formula: ext{Perimeter} = 2 imes ext{length} + 2 imes ext{width}

  • Trapezoid:

  • Formula: ext{Perimeter} = ext{side}1 + ext{side}2 + ext{side}3 + ext{side}4

Area of Quadrilaterals

• The area of a quadrilateral is defined as the amount of space contained within its boundaries.

• Formulas for Area:

  • Square:

  • Formula: ext{Area} = ext{length}^2

  • Rectangle:

  • Formula: ext{Area} = ext{length} imes ext{height}

  • Parallelogram:

  • Formula: ext{Area} = ext{base} imes ext{height}

  • Trapezoid:

  • Formula: ext{Area} = rac{( ext{base}1 + ext{base}2) imes ext{height}}{2}

Changes in Dimensions

• A change in dimensions results in different impacts on perimeter and area:

  • Perimeter: Changes are directly proportional to the change in dimensions.

  • Example: If the dimensions are doubled, the perimeter also doubles.

  • Area: Changes are proportional to the square of the change in dimensions.

  • Example: If the dimensions are doubled, the area will be multiplied by (2^2) = 4.

Congruent and Similar Quadrilaterals

• Congruent Quadrilaterals:

  • Definition: Quadrilaterals that are identical in terms of side lengths and angles.

  • Note: The only possible differences between them may be their location or orientation in space.

• Similar Quadrilaterals:

  • Definition: Quadrilaterals that have the same angle measurements and proportional lengths of corresponding sides.